Data Science Engineer at DataSource.ai
The popularity of data science attracts a lot of people from a wide range of professions to make a career change with the goal of becoming a data scientist.Despite the high demand for data scientists, it is a highly challenging task to find your first job. Unless you have a solid prior job experience, interviews are where you can show you skills and impress your potential employer.Data science is an interdisciplinary field which covers a broad range of topics and concepts. Thus, the number of questions that you might be asked at an interview is very high.However, there are some questions about the fundamentals in data science and machine learning. These are the ones you do not want to miss. In this article, we will go over 10 questions that are likely to be asked at a data scientist interview.The questions are grouped into 3 main categories which are machine learning, Python, and SQL. I will try to provide a brief answer for each question. However, I suggest reading or studying each one in more detail afterwards.Machine Learning1. What is overfitting?Overfitting in machine learning occurs when your model is not generalized well. The model is too focused on the training set. It captures a lot of detail or even noise in the training set. Thus, it fails to capture the general trend or the relationships in the data. If a model is too complex compared to the data, it will probably be overfitting.A strong indicator of overfitting is the high difference between the accuracy of training and test sets. Overfit models usually have very high accuracy on the training set but the test accuracy is usually unpredictable and much lower than the training accuracy.2. How can you reduce overfitting?We can reduce overfitting by making the model more generalized which means it should be more focused on the general trend rather than specific details.If it is possible, collecting more data is an efficient way to reduce overfitting. You will be giving more juice to the model so it will have more material to learn from. Data is always valuable especially for machine learning models.Another method to reduce overfitting is to reduce the complexity of the model. If a model is too complex for a given task, it will likely result in overfitting. In such cases, we should look for simpler models.3. What is regularization?We have mentioned that the main reason for overfitting is a model being more complex than necessary. Regularization is a method for reducing the model complexity.It does so by penalizing higher terms in the model. With the addition of a regularization term, the model tries to minimize both loss and complexity.Two main types of regularization are L1 and L2 regularization. L1 regularization subtracts a small amount from the weights of uninformative features at each iteration. Thus, it causes these weights to eventually become zero.On the other hand, L2 regularization removes a small percentage from the weights at each iteration. These weights will get closer to zero but never actually become 0.4. What is the difference between classification and clustering?Both are machine learning tasks. Classification is a supervised learning task so we have labelled observations (i.e. data points). We train a model with labelled data and expect it to predict the labels of new data.For instance, spam email detection is a classification task. We provide a model with several emails marked as spam or not spam. After the model is trained with those emails, it will evaluate the new emails appropriately.Clustering is an unsupervised learning task so the observations do not have any labels. The model is expected to evaluate the observations and group them into clusters. Similar observations are placed into the same cluster.In the optimal case, the observations in the same cluster are as close to each other as possible and the different clusters are as far apart as possible. An example of a clustering task would be grouping customers based on their shopping behavior.PythonThe built-in data structures are of crucial importance. Thus, you should be familiar with what they are and how to interact with them. List, dictionary, set, and tuple are 4 main built-in data structures in Python.5. What is the difference between lists and tuplesThe main difference between lists and tuples is mutability. Lists are mutable so we can manipulate them by adding or removing items.mylist = [1,2,3] mylist.append(4) mylist.remove(1) print(mylist) [2,3,4]On the other hand, tuples are immutable. Although we can access each element in a tuple, we cannot modify its content.mytuple = (1,2,3) mytuple.append(4) AttributeError: 'tuple' object has no attribute 'append'One important point to mention here is that although tuples are immutable, they can contain mutable elements such as lists or sets.mytuple = (1,2,["a","b","c"]) mytuple[2] ['a', 'b', 'c'] mytuple[2][0] = ["A"] print(mytuple) (1, 2, [['A'], 'b', 'c'])6. What is the difference between lists and setsLet’s do an example to demonstrate the main difference between lists and sets.text = "Python is awesome!" mylist = list(text) myset = set(text) print(mylist) ['P', 'y', 't', 'h', 'o', 'n', ' ', 'i', 's', ' ', 'a', 'w', 'e', 's', 'o', 'm', 'e', '!'] print(myset) {'t', ' ', 'i', 'e', 'm', 'P', '!', 'y', 'o', 'h', 'n', 'a', 's', 'w'}As we notice in the resulting objects, the list contains all the characters in the string whereas the set only contains unique values.Another difference is that the characters in the list are ordered based on their location in the string. However, there is no order associated with the characters in the set.Here is a table that summarizes the main characteristics of lists, tuples, and sets.(image by author)7. What is a dictionary and what are the important features of dictionaries?A dictionary in Python is a collection of key-value pairs. It is similar to a list in the sense that each item in a list has an associated index starting from 0.mylist = ["a", "b", "c"] mylist[1] "b"In a dictionary, we have keys as the index. Thus, we can access a value by using its key.mydict = {"John": 24, "Jane": 26, "Ashley": 22} mydict["Jane"] 26The keys in a dictionary are unique which makes sense because they act like an address for the values.SQLSQL is an extremely important skill for data scientists. There are quite a number of companies that store their data in a relational database. SQL is what is needed to interact with relational databases.You will probably be asked a question that involves writing a query to perform a specific task. You might also be asked a question about general database knowledge.8. Query example 1Consider we have a sales table that contains daily sales quantities of products.SELECT TOP 10 * FROM SalesTable(image by author)Find the top 5 weeks in terms of total weekly sales quantities.SELECT TOP 5 CONCAT(YEAR(SalesDate), DATEPART(WEEK, SalesDate)) AS YearWeek, SUM(SalesQty) AS TotalWeeklySales FROM SalesTable GROUP BY CONCAT(YEAR(SalesDate), DATEPART(WEEK, SalesDate)) ORDER BY TotalWeeklySales DESC (image by author)We first extract the year and week information from the date column and then use it in the aggregation. The sum function is used to calculate the total sales quantities.9. Query example 2In the same sales table, find the number of unique items that are sold each month.SELECT MONTH(SalesDate) AS Month, COUNT(DISTINCT(ItemNumber)) AS ItemCount FROM SalesTable GROUP BY MONTH(SalesDate) Month ItemCount 1 9 1021 2 8 102110. What is normalization and denormalization in a database?These terms are related to database schema design. Normalization and denormalization aim to optimize different metrics.The goal of normalization is to reduce data redundancy and inconsistency by increasing the number of tables. On the other hand, denormalization aims to speed up the query execution. Denormalization decreases the number of tables but at the same time, it adds some redundancy.ConclusionIt is a challenging task to become a data scientist. It requires time, effort, and dedication. Without having prior job experience, the process gets harder.Interviews are very important to demonstrate your skills. In this article, we have covered 10 questions that you are likely to encounter in a data scientist interview.Thank you for reading. Please let me know if you have any feedback.Soner Yıldırım
Apr 06, 2021
The article contains some of the most commonly used advanced statistical concepts along with their Python implementation.In my previous articles Beginners Guide to Statistics in Data Science and The Inferential Statistics Data Scientists Should Know we have talked about almost all the basics(Descriptive and Inferential) of statistics which are commonly used in understanding and working with any data science case study. In this article, lets go a little beyond and talk about some advance concepts which are not part of the buzz.Concept #1 - Q-Q(quantile-quantile) PlotsBefore understanding QQ plots first understand what is a Quantile?A quantile defines a particular part of a data set, i.e. a quantile determines how many values in a distribution are above or below a certain limit. Special quantiles are the quartile (quarter), the quintile (fifth), and percentiles (hundredth).An example:If we divide a distribution into four equal portions, we will speak of four quartiles. The first quartile includes all values that are smaller than a quarter of all values. In a graphical representation, it corresponds to 25% of the total area of distribution. The two lower quartiles comprise 50% of all distribution values. The interquartile range between the first and third quartile equals the range in which 50% of all values lie that are distributed around the mean. In Statistics, A Q-Q(quantile-quantile) plot is a scatterplot created by plotting two sets of quantiles against one another. If both sets of quantiles came from the same distribution, we should see the points forming a line that’s roughly straight(y=x).Q-Q plotFor example, the median is a quantile where 50% of the data fall below that point and 50% lie above it. The purpose of Q Q plots is to find out if two sets of data come from the same distribution. A 45-degree angle is plotted on the Q Q plot; if the two data sets come from a common distribution, the points will fall on that reference line.It’s very important for you to know whether the distribution is normal or not so as to apply various statistical measures on the data and interpret it in much more human-understandable visualization and their Q-Q plot comes into the picture. The most fundamental question answered by the Q-Q plot is if the curve is Normally Distributed or not.Normally distributed, but why?The Q-Q plots are used to find the type of distribution for a random variable whether it is a Gaussian Distribution, Uniform Distribution, Exponential Distribution, or even Pareto Distribution, etc. You can tell the type of distribution using the power of the Q-Q plot just by looking at the plot. In general, we are talking about Normal distributions only because we have a very beautiful concept of the 68–95–99.7 rule which perfectly fits into the normal distribution So we know how much of the data lies in the range of the first standard deviation, second standard deviation and third standard deviation from the mean. So knowing if a distribution is Normal opens up new doors for us to experiment with Types of Q-Q plots. Source Skewed Q-Q plotsQ-Q plots can find skewness(measure of asymmetry) of the distribution. If the bottom end of the Q-Q plot deviates from the straight line but the upper end is not, then the distribution is Left skewed(Negatively skewed).Now if upper end of the Q-Q plot deviates from the staright line and the lower is not, then the distribution is Right skewed(Positively skewed).Tailed Q-Q plotsQ-Q plots can find Kurtosis(measure of tailedness) of the distribution.The distribution with the fat tail will have both the ends of the Q-Q plot to deviate from the straight line and its centre follows the line, where as a thin tailed distribution will term Q-Q plot with very less or negligible deviation at the ends thus making it a perfect fit for normal distribution.Q-Q plots in Python(Source)Suppose we have the following dataset of 100 values:import numpy as np #create dataset with 100 values that follow a normal distribution np.random.seed(0) data = np.random.normal(0,1, 1000) #view first 10 values data[:10] array([ 1.76405235, 0.40015721, 0.97873798, 2.2408932 , 1.86755799, -0.97727788, 0.95008842, -0.15135721, -0.10321885, 0.4105985 ])To create a Q-Q plot for this dataset, we can use the qqplot() function from the statsmodels library:import statsmodels.api as sm import matplotlib.pyplot as plt #create Q-Q plot with 45-degree line added to plot fig = sm.qqplot(data, line='45') plt.show()In a Q-Q plot, the x-axis displays the theoretical quantiles. This means it doesn’t show your actual data, but instead, it represents where your data would be if it were normally distributed.The y-axis displays your actual data. This means that if the data values fall along a roughly straight line at a 45-degree angle, then the data is normally distributed.We can see in our Q-Q plot above that the data values tend to closely follow the 45-degree, which means the data is likely normally distributed. This shouldn’t be surprising since we generated the 100 data values by using the numpy.random.normal() function.Consider instead if we generated a dataset of 100 uniformly distributed values and created a Q-Q plot for that dataset:#create dataset of 100 uniformally distributed values data = np.random.uniform(0,1, 1000) #generate Q-Q plot for the dataset fig = sm.qqplot(data, line='45') plt.show()The data values clearly do not follow the red 45-degree line, which is an indication that they do not follow a normal distribution.Concept #2- Chebyshev's InequalityIn probability, Chebyshev’s Inequality, also known as “Bienayme-Chebyshev” Inequality guarantees that, for a wide class of probability distributions, only a definite fraction of values will be found within a specific distance from the mean of a distribution.Source: https://www.thoughtco.com/chebyshevs-inequality-3126547 Chebyshev’s inequality is similar to The Empirical rule(68-95-99.7); however, the latter rule only applies to normal distributions. Chebyshev’s inequality is broader; it can be applied to any distribution so long as the distribution includes a defined variance and mean.So Chebyshev’s inequality says that at least (1-1/k^2) of data from a sample must fall within K standard deviations from the mean (or equivalently, no more than 1/k^2 of the distribution’s values can be more than k standard deviations away from the mean).Where K --> Positive real numberIf the data is not normally distributed then different amounts of data could be in one standard deviation. Chebyshev’s inequality provides a way to know what fraction of data falls within K standard deviations from the mean for any data distribution.Also read: 22 Statistics Questions to Prepare for Data Science InterviewsCredits: https://calcworkshop.com/joint-probability-distribution/chebyshev-inequality/ Chebyshev’s inequality is of great value because it can be applied to any probability distribution in which the mean and variance are provided.Let us consider an example, Assume 1,000 contestants show up for a job interview, but there are only 70 positions available. In order to select the finest 70 contestants amongst the total contestants, the proprietor gives tests to judge their potential. The mean score on the test is 60, with a standard deviation of 6. If an applicant scores an 84, can they presume that they are getting the job?The results show that about 63 people scored above a 60, so with 70 positions available, a contestant who scores an 84 can be assured they got the job.Chebyshev's Inequality in Python(Source) Create a population of 1,000,000 values, I use a gamma distribution(also works with other distributions) with shape = 2 and scale = 2.import numpy as np import random import matplotlib.pyplot as plt #create a population with a gamma distribution shape, scale = 2., 2. #mean=4, std=2*sqrt(2) mu = shape*scale #mean and standard deviation sigma = scale*np.sqrt(shape) s = np.random.gamma(shape, scale, 1000000)Now sample 10,000 values from the population.#sample 10000 values rs = random.choices(s, k=10000)Count the sample that has a distance from the expected value larger than k standard deviation and use the count to calculate the probabilities. I want to depict a trend of probabilities when k is increasing, so I use a range of k from 0.1 to 3.#set k ks = [0.1,0.5,1.0,1.5,2.0,2.5,3.0] #probability list probs = [] #for each k for k in ks: #start count c = 0 for i in rs: # count if far from mean in k standard deviation if abs(i - mu) > k * sigma : c += 1 probs.append(c/10000)Plot the results:plot = plt.figure(figsize=(20,10)) #plot each probability plt.xlabel('K') plt.ylabel('probability') plt.plot(ks,probs, marker='o') plot.show() #print each probability print("Probability of a sample far from mean more than k standard deviation:") for i, prob in enumerate(probs): print("k:" + str(ks[i]) + ", probability: " \ + str(prob)[0:5] + \ " | in theory, probability should less than: " \ + str(1/ks[i]**2)[0:5])From the above plot and result, we can see that as the k increases, the probability is decreasing, and the probability of each k follows the inequality. Moreover, only the case that k is larger than 1 is useful. If k is less than 1, the right side of the inequality is larger than 1 which is not useful because the probability cannot be larger than 1.Concept #3- Log-Normal DistributionIn probability theory, a Log-normal distribution also known as Galton's distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution. Equivalently, if Y has a normal distribution, then the exponential function of Y i.e, X = exp(Y), has a log-normal distribution. Skewed distributions with low mean and high variance and all positive values fit under this type of distribution. A random variable that is log-normally distributed takes only positive real values. The general formula for the probability density function of the lognormal distribution is:The location and scale parameters are equivalent to the mean and standard deviation of the logarithm of the random variable.The shape of Lognormal distribution is defined by 3 parameters:σis the shape parameter, (and is the standard deviation of the log of the distribution)θ or μ is the location parameter (and is the mean of the distribution)m is the scale parameter (and is also the median of the distribution)The location and scale parameters are equivalent to the mean and standard deviation of the logarithm of the random variable as explained above.If x = θ, then f(x) = 0. The case where θ = 0 and m = 1 is called the standard lognormal distribution. The case where θ equals zero is called the 2-parameter lognormal distribution.The following graph illustrates the effect of the location(μ) and scale(σ) parameter on the probability density function of the lognormal distribution: Source: https://www.sciencedirect.com/topics/mathematics/lognormal-distribution Log-Normal Distribution in Python(Source)Let us consider an example to generate random numbers from a log-normal distribution with μ=1 and σ=0.5 using scipy.stats.lognorm function.import numpy as np import matplotlib.pyplot as plt from scipy.stats import lognorm np.random.seed(42) data = lognorm.rvs(s=0.5, loc=1, scale=1000, size=1000) plt.figure(figsize=(10,6)) ax = plt.subplot(111) plt.title('Generate wrandom numbers from a Log-normal distribution') ax.hist(data, bins=np.logspace(0,5,200), density=True) ax.set_xscale("log") shape,loc,scale = lognorm.fit(data) x = np.logspace(0, 5, 200) pdf = lognorm.pdf(x, shape, loc, scale) ax.plot(x, pdf, 'y') plt.show()Concept #4- Power Law distributionIn statistics, a Power Law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four.A power law distribution has the form Y = k Xα, where:X and Y are variables of interest,α is the law’s exponent,k is a constant.Source: https://en.wikipedia.org/wiki/Power_law Power-law distribution is just one of many probability distributions, but it is considered a valuable tool to assess uncertainty issues that normal distribution cannot handle when they occur at a certain probability.Many processes have been found to follow power laws over substantial ranges of values. From the distribution in incomes, size of meteoroids, earthquake magnitudes, the spectral density of weight matrices in deep neural networks, word usage, number of neighbors in various networks, etc. (Note: The power law here is a continuous distribution. The last two examples are discrete, but on a large scale can be modeled as if continuous).Also read: Statistical Measures of Central TendencyPower-law distribution in Python(Source) Let us plot the Pareto distribution which is one form of a power-law probability distribution. Pareto distribution is sometimes known as the Pareto Principle or ‘80–20’ rule, as the rule states that 80% of society’s wealth is held by 20% of its population. Pareto distribution is not a law of nature, but an observation. It is useful in many real-world problems. It is a skewed heavily tailed distribution.import numpy as np import matplotlib.pyplot as plt from scipy.stats import pareto x_m = 1 #scale alpha = [1, 2, 3] #list of values of shape parameters plt.figure(figsize=(10,6)) samples = np.linspace(start=0, stop=5, num=1000) for a in alpha: output = np.array([pareto.pdf(x=samples, b=a, loc=0, scale=x_m)]) plt.plot(samples, output.T, label='alpha {0}' .format(a)) plt.xlabel('samples', fontsize=15) plt.ylabel('PDF', fontsize=15) plt.title('Probability Density function', fontsize=15) plt.legend(loc='best') plt.show()Concept #5- Box cox transformationThe Box-Cox transformation transforms our data so that it closely resembles a normal distribution.The one-parameter Box-Cox transformations are defined as In many statistical techniques, we assume that the errors are normally distributed. This assumption allows us to construct confidence intervals and conduct hypothesis tests. By transforming your target variable, we can (hopefully) normalize our errors (if they are not already normal).Additionally, transforming our variables can improve the predictive power of our models because transformations can cut away white noise.Original distribution(Left) and near-normal distribution after applying Box cox transformation. Source At the core of the Box-Cox transformation is an exponent, lambda (λ), which varies from -5 to 5. All values of λ are considered and the optimal value for your data is selected; The “optimal value” is the one that results in the best approximation of a normal distribution curve. The one-parameter Box-Cox transformations are defined as:and the two-parameter Box-Cox transformations as:Moreover, the one-parameter Box-Cox transformation holds for y > 0, i.e. only for positive values and two-parameter Box-Cox transformation for y > -λ, i.e. negative values. The parameter λ is estimated using the profile likelihood function and using goodness-of-fit tests.If we talk about some drawbacks of Box-cox transformation, then if interpretation is what you want to do, then Box-cox is not recommended. Because if λ is some non-zero number, then the transformed target variable may be more difficult to interpret than if we simply applied a log transform.A second stumbling block is that the Box-Cox transformation usually gives the median of the forecast distribution when we revert the transformed data to its original scale. Occasionally, we want the mean and not the median.Box-Cox transformation in Python(Source)SciPy’s stats package provides a function called boxcox for performing box-cox power transformation that takes in original non-normal data as input and returns fitted data along with the lambda value that was used to fit the non-normal distribution to normal distribution.#load necessary packages import numpy as np from scipy.stats import boxcox import seaborn as sns #make this example reproducible np.random.seed(0) #generate dataset data = np.random.exponential(size=1000) fig, ax = plt.subplots(1, 2) #plot the distribution of data values sns.distplot(data, hist=False, kde=True, kde_kws = {'shade': True, 'linewidth': 2}, label = "Non-Normal", color ="red", ax = ax[0]) #perform Box-Cox transformation on original data transformed_data, best_lambda = boxcox(data) sns.distplot(transformed_data, hist = False, kde = True, kde_kws = {'shade': True, 'linewidth': 2}, label = "Normal", color ="red", ax = ax[1]) #adding legends to the subplots plt.legend(loc = "upper right") #rescaling the subplots fig.set_figheight(5) fig.set_figwidth(10) #display optimal lambda value print(f"Lambda value used for Transformation: {best_lambda}") Concept #6- Poisson distributionIn probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.In very simple terms, A Poisson distribution can be used to estimate how likely it is that something will happen "X" number of times. Some examples of Poisson processes are customers calling a help center, radioactive decay in atoms, visitors to a website, photons arriving at a space telescope, and movements in a stock price. Poisson processes are usually associated with time, but they do not have to be. The Formula for the Poisson Distribution Is:Where:e is Euler's number (e = 2.71828...)k is the number of occurrencesk! is the factorial of kλ is equal to the expected value of kwhen that is also equal to its varianceLambda(λ) can be thought of as the expected number of events in the interval. As we change the rate parameter, λ, we change the probability of seeing different numbers of events in one interval. The below graph is the probability mass function of the Poisson distribution showing the probability of a number of events occurring in an interval with different rate parameters. Probability Mass function for Poisson Distribution with varying rate parameters.Source The Poisson distribution is also commonly used to model financial count data where the tally is small and is often zero. For one example, in finance, it can be used to model the number of trades that a typical investor will make in a given day, which can be 0 (often), or 1, or 2, etc.As another example, this model can be used to predict the number of "shocks" to the market that will occur in a given time period, say over a decade.Poisson distribution in Pythonfrom numpy import random import matplotlib.pyplot as plt import seaborn as sns lam_list = [1, 4, 9] #list of Lambda values plt.figure(figsize=(10,6)) samples = np.linspace(start=0, stop=5, num=1000) for lam in lam_list: sns.distplot(random.poisson(lam=lam, size=10), hist=False, label='lambda {0}'.format(lam)) plt.xlabel('Poisson Distribution', fontsize=15) plt.ylabel('Frequency', fontsize=15) plt.legend(loc='best') plt.show()As λ becomes bigger, the graph looks more like a normal distribution.I hope you have enjoyed reading this article, If you have any questions or suggestions, please leave a comment. Also read: False Positives vs. False NegativesFeel free to connect me on LinkedIn for any query.Thanks for reading!!!Referenceshttps://calcworkshop.com/joint-probability-distribution/chebyshev-inequality/ https://corporatefinanceinstitute.com/resources/knowledge/data-analysis/chebyshevs-inequality/ https://www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm https://www.statology.org/q-q-plot-python/ https://gist.github.com/chaipi-chaya/9eb72978dbbfd7fa4057b493cf6a32e7 https://stackoverflow.com/a/41968334/7175247
Apr 06, 2021
CreditsPredictive models have become a trusted advisor to many businesses and for a good reason. These models can “foresee the future”, and there are many different methods available, meaning any industry can find one that fits their particular challenges.When we talk about predictive models, we are talking either about a regression model (continuous output) or a classification model (nominal or binary output). In classification problems, we use two types of algorithms (dependent on the kind of output it creates):Class output: Algorithms like SVM and KNN create a class output. For instance, in a binary classification problem, the outputs will be either 0 or 1. However, today we have algorithms that can convert these class outputs to probability.Probability output: Algorithms like Logistic Regression, Random Forest, Gradient Boosting, Adaboost, etc. give probability outputs. Converting probability outputs to class output is just a matter of creating a threshold probability.IntroductionWhile data preparation and training a machine learning model is a key step in the machine learning pipeline, it’s equally important to measure the performance of this trained model. How well the model generalizes on the unseen data is what defines adaptive vs non-adaptive machine learning models.By using different metrics for performance evaluation, we should be in a position to improve the overall predictive power of our model before we roll it out for production on unseen data.Without doing a proper evaluation of the ML model using different metrics, and depending only on accuracy, it can lead to a problem when the respective model is deployed on unseen data and can result in poor predictions.This happens because, in cases like these, our models don’t learn but instead memorize;hence, they cannot generalize well on unseen data.Model Evaluation MetricsLet us now define the evaluation metrics for evaluating the performance of a machine learning model, which is an integral component of any data science project. It aims to estimate the generalization accuracy of a model on the future (unseen/out-of-sample) data.Confusion MatrixA confusion matrix is a matrix representation of the prediction results of any binary testing that is often used to describe the performance of the classification model (or “classifier”) on a set of test data for which the true values are known.The confusion matrix itself is relatively simple to understand, but the related terminology can be confusing.Confusion matrix with 2 class labels.Each prediction can be one of the four outcomes, based on how it matches up to the actual value:True Positive (TP): Predicted True and True in reality.True Negative (TN): Predicted False and False in reality.False Positive (FP): Predicted True and False in reality.False Negative (FN): Predicted False and True in reality.Now let us understand this concept using hypothesis testing.A Hypothesis is speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false.A Null Hypothesis is a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove.We would always reject the null hypothesis when it is false, and we would accept the null hypothesis when it is indeed true.Even though hypothesis tests are meant to be reliable, there are two types of errors that can occur.These errors are known as Type 1 and Type II errors.For example, when examining the effectiveness of a drug, the null hypothesis would be that the drug does not affect a disease.Type I Error:- equivalent to False Positives(FP).The first kind of error that is possible involves the rejection of a null hypothesis that is true.Let’s go back to the example of a drug being used to treat a disease. If we reject the null hypothesis in this situation, then we claim that the drug does have some effect on a disease. But if the null hypothesis is true, then, in reality, the drug does not combat the disease at all. The drug is falsely claimed to have a positive effect on a disease.Type II Error:- equivalent to False Negatives(FN).The other kind of error that occurs when we accept a false null hypothesis. This sort of error is called a type II error and is also referred to as an error of the second kind.If we think back again to the scenario in which we are testing a drug, what would a type II error look like? A type II error would occur if we accepted that the drug hs no effect on disease, but in reality, it did.A sample python implementation of the Confusion matrix.import warnings import pandas as pd from sklearn import model_selection from sklearn.linear_model import LogisticRegression from sklearn.metrics import confusion_matrix import matplotlib.pyplot as plt %matplotlib inline #ignore warnings warnings.filterwarnings('ignore') # Load digits dataset url = "http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data" df = pd.read_csv(url) # df = df.values X = df.iloc[:,0:4] y = df.iloc[:,4] #test size test_size = 0.33 #generate the same set of random numbers seed = 7 #Split data into train and test set. X_train, X_test, y_train, y_test = model_selection.train_test_split(X, y, test_size=test_size, random_state=seed) #Train Model model = LogisticRegression() model.fit(X_train, y_train) pred = model.predict(X_test) #Construct the Confusion Matrix labels = ['Iris-setosa', 'Iris-versicolor', 'Iris-virginica'] cm = confusion_matrix(y_test, pred, labels) print(cm) fig = plt.figure() ax = fig.add_subplot(111) cax = ax.matshow(cm) plt.title('Confusion matrix') fig.colorbar(cax) ax.set_xticklabels([''] + labels) ax.set_yticklabels([''] + labels) plt.xlabel('Predicted Values') plt.ylabel('Actual Values') plt.show()Confusion matrix with 3 class labels.The diagonal elements represent the number of points for which the predicted label is equal to the true label, while anything off the diagonal was mislabeled by the classifier. Therefore, the higher the diagonal values of the confusion matrix the better, indicating many correct predictions.In our case, the classifier predicted all the 13 setosa and 18 virginica plants in the test data perfectly. However, it incorrectly classified 4 of the versicolor plants as virginica.There is also a list of rates that are often computed from a confusion matrix for a binary classifier:1. AccuracyOverall, how often is the classifier correct?Accuracy = (TP+TN)/totalWhen our classes are roughly equal in size, we can use accuracy, which will give us correctly classified values.Accuracy is a common evaluation metric for classification problems. It’s the number of correct predictions made as a ratio of all predictions made.Misclassification Rate(Error Rate): Overall, how often is it wrong. Since accuracy is the percent we correctly classified (success rate), it follows that our error rate (the percentage we got wrong) can be calculated as follows:Misclassification Rate = (FP+FN)/totalWe use the sklearn module to compute the accuracy of a classification task, as shown below.#import modules import warnings import pandas as pd import numpy as np from sklearn import model_selection from sklearn.linear_model import LogisticRegression from sklearn import datasets from sklearn.metrics import accuracy_score #ignore warnings warnings.filterwarnings('ignore') # Load digits dataset iris = datasets.load_iris() # # Create feature matrix X = iris.data # Create target vector y = iris.target #test size test_size = 0.33 #generate the same set of random numbers seed = 7 #cross-validation settings kfold = model_selection.KFold(n_splits=10, random_state=seed) #Model instance model = LogisticRegression() #Evaluate model performance scoring = 'accuracy' results = model_selection.cross_val_score(model, X, y, cv=kfold, scoring=scoring) print('Accuracy -val set: %.2f%% (%.2f)' % (results.mean()*100, results.std())) #split data X_train, X_test, y_train, y_test = model_selection.train_test_split(X, y, test_size=test_size, random_state=seed) #fit model model.fit(X_train, y_train) #accuracy on test set result = model.score(X_test, y_test) print("Accuracy - test set: %.2f%%" % (result*100.0))The classification accuracy is 88% on the validation set.2. PrecisionWhen it predicts yes, how often is it correct?Precision=TP/predicted yesWhen we have a class imbalance, accuracy can become an unreliable metric for measuring our performance. For instance, if we had a 99/1 split between two classes, A and B, where the rare event, B, is our positive class, we could build a model that was 99% accurate by just saying everything belonged to class A. Clearly, we shouldn’t bother building a model if it doesn’t do anything to identify class B; thus, we need different metrics that will discourage this behavior. For this, we use precision and recall instead of accuracy.3. Recall or SensitivityWhen it’s actually yes, how often does it predict yes?True Positive Rate = TP/actual yesRecall gives us the true positive rate (TPR), which is the ratio of true positives to everything positive.In the case of the 99/1 split between classes A and B, the model that classifies everything as A would have a recall of 0% for the positive class, B (precision would be undefined — 0/0). Precision and recall provide a better way of evaluating model performance in the face of a class imbalance. They will correctly tell us that the model has little value for our use case.Just like accuracy, both precision and recall are easy to compute and understand but require thresholds. Besides, precision and recall only consider half of the confusion matrix:4. F1 ScoreThe F1 score is the harmonic mean of the precision and recall, where an F1 score reaches its best value at 1 (perfect precision and recall) and worst at 0.Why harmonic mean? Since the harmonic mean of a list of numbers skews strongly toward the least elements of the list, it tends (compared to the arithmetic mean) to mitigate the impact of large outliers and aggravate the impact of small ones.An F1 score punishes extreme values more. Ideally, an F1 Score could be an effective evaluation metric in the following classification scenarios:When FP and FN are equally costly — meaning they miss on true positives or find false positives — both impact the model almost the same way, as in our cancer detection classification exampleAdding more data doesn’t effectively change the outcome effectivelyTN is high (like with flood predictions, cancer predictions, etc.)A sample python implementation of the F1 score.import warnings import pandas from sklearn import model_selection from sklearn.linear_model import LogisticRegression from sklearn.metrics import log_loss from sklearn.metrics import precision_recall_fscore_support as score, precision_score, recall_score, f1_score warnings.filterwarnings('ignore') url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" dataframe = pandas.read_csv(url) dat = dataframe.values X = dat[:,:-1] y = dat[:,-1] test_size = 0.33 seed = 7 model = LogisticRegression() #split data X_train, X_test, y_train, y_test = model_selection.train_test_split(X, y, test_size=test_size, random_state=seed) model.fit(X_train, y_train) precision = precision_score(y_test, pred) print('Precision: %f' % precision) # recall: tp / (tp + fn) recall = recall_score(y_test, pred) print('Recall: %f' % recall) # f1: tp / (tp + fp + fn) f1 = f1_score(y_test, pred) print('F1 score: %f' % f1)5. SpecificityWhen it’s no, how often does it predict no?True Negative Rate=TN/actual noIt is the true negative rate or the proportion of true negatives to everything that should have been classified as negative.Note that, together, specificity and sensitivity consider the full confusion matrix:6. Receiver Operating Characteristics (ROC) CurveMeasuring the area under the ROC curve is also a very useful method for evaluating a model. By plotting the true positive rate (sensitivity) versus the false-positive rate (1 — specificity), we get the Receiver Operating Characteristic (ROC) curve. This curve allows us to visualize the trade-off between the true positive rate and the false positive rate.The following are examples of good ROC curves. The dashed line would be random guessing (no predictive value) and is used as a baseline; anything below that is considered worse than guessing. We want to be toward the top-left corner:A sample python implementation of the ROC curves.#Classification Area under curve import warnings import pandas from sklearn import model_selection from sklearn.linear_model import LogisticRegression from sklearn.metrics import roc_auc_score, roc_curve warnings.filterwarnings('ignore') url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" dataframe = pandas.read_csv(url) dat = dataframe.values X = dat[:,:-1] y = dat[:,-1] seed = 7 #split data X_train, X_test, y_train, y_test = model_selection.train_test_split(X, y, test_size=test_size, random_state=seed) model.fit(X_train, y_train) # predict probabilities probs = model.predict_proba(X_test) # keep probabilities for the positive outcome only probs = probs[:, 1] auc = roc_auc_score(y_test, probs) print('AUC - Test Set: %.2f%%' % (auc*100)) # calculate roc curve fpr, tpr, thresholds = roc_curve(y_test, probs) # plot no skill plt.plot([0, 1], [0, 1], linestyle='--') # plot the roc curve for the model plt.plot(fpr, tpr, marker='.') plt.xlabel('False positive rate') plt.ylabel('Sensitivity/ Recall') # show the plot plt.show()In the example above, the AUC is relatively close to 1 and greater than 0.5. A perfect classifier will have the ROC curve go along the Y-axis and then along the X-axisLog LossLog Loss is the most important classification metric based on probabilities.As the predicted probability of the true class gets closer to zero, the loss increases exponentially:It measures the performance of a classification model where the prediction input is a probability value between 0 and 1. Log loss increases as the predicted probability diverge from the actual label. The goal of any machine learning model is to minimize this value. As such, smaller log loss is better, with a perfect model having a log loss of 0.A sample python implementation of the Log Loss.#Classification LogLoss import warnings import pandas from sklearn import model_selection from sklearn.linear_model import LogisticRegression from sklearn.metrics import log_loss warnings.filterwarnings('ignore') url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv" dataframe = pandas.read_csv(url) dat = dataframe.values X = dat[:,:-1] y = dat[:,-1] seed = 7 #split data X_train, X_test, y_train, y_test = model_selection.train_test_split(X, y, test_size=test_size, random_state=seed) model.fit(X_train, y_train) #predict and compute logloss pred = model.predict(X_test) accuracy = log_loss(y_test, pred) print("Logloss: %.2f" % (accuracy))Logloss: 8.02 Jaccard IndexJaccard Index is one of the simplest ways to calculate and find out the accuracy of a classification ML model. Let’s understand it with an example. Suppose we have a labeled test set, with labels as –y = [0,0,0,0,0,1,1,1,1,1]And our model has predicted the labels as –y1 = [1,1,0,0,0,1,1,1,1,1]The above Venn diagram shows us the labels of the test set and the labels of the predictions, and their intersection and union.Jaccard Index or Jaccard similarity coefficient is a statistic used in understanding the similarities between sample sets. The measurement emphasizes the similarity between finite sample sets and is formally defined as the size of the intersection divided by the size of the union of the two labeled sets, with formula as –Jaccard Index or Intersection over Union(IoU)So, for our example, we can see that the intersection of the two sets is equal to 8 (since eight values are predicted correctly) and the union is 10 + 10–8 = 12. So, the Jaccard index gives us the accuracy as –So, the accuracy of our model, according to Jaccard Index, becomes 0.66, or 66%.Higher the Jaccard index higher the accuracy of the classifier.A sample python implementation of the Jaccard index.import numpy as np def compute_jaccard_similarity_score(x, y): intersection_cardinality = len(set(x).intersection(set(y))) union_cardinality = len(set(x).union(set(y))) return intersection_cardinality / float(union_cardinality) score = compute_jaccard_similarity_score(np.array([0, 1, 2, 5, 6]), np.array([0, 2, 3, 5, 7, 9])) print "Jaccard Similarity Score : %s" %score passJaccard Similarity Score : 0.375Kolomogorov Smirnov chartK-S or Kolmogorov-Smirnov chart measures the performance of classification models. More accurately, K-S is a measure of the degree of separation between positive and negative distributions.The cumulative frequency for the observed and hypothesized distributions is plotted against the ordered frequencies. The vertical double arrow indicates the maximal vertical difference.The K-S is 100 if the scores partition the population into two separate groups in which one group contains all the positives and the other all the negatives. On the other hand, If the model cannot differentiate between positives and negatives, then it is as if the model selects cases randomly from the population. The K-S would be 0.In most classification models the K-S will fall between 0 and 100, and that the higher the value the better the model is at separating the positive from negative cases.The K-S may also be used to test whether two underlying one-dimensional probability distributions differ. It is a very efficient way to determine if two samples are significantly different from each other.A sample python implementation of the Kolmogorov-Smirnov.from scipy.stats import kstest import random # N = int(input("Enter number of random numbers: ")) N = 10 actual =[] print("Enter outcomes: ") for i in range(N): # x = float(input("Outcomes of class "+str(i + 1)+": ")) actual.append(random.random()) print(actual) x = kstest(actual, "norm") print(x)The Null hypothesis used here assumes that the numbers follow the normal distribution. It returns statistics and p-value. If the p-value is < alpha, we reject the Null hypothesis.Alpha is defined as the probability of rejecting the null hypothesis given the null hypothesis(H0) is true. For most of the practical applications, alpha is chosen as 0.05.Gain and Lift ChartGain or Lift is a measure of the effectiveness of a classification model calculated as the ratio between the results obtained with and without the model. Gain and lift charts are visual aids for evaluating the performance of classification models. However, in contrast to the confusion matrix that evaluates models on the whole population gain or lift chart evaluates model performance in a portion of the population.The higher the lift (i.e. the further up it is from the baseline), the better the model.The following gains chart, run on a validation set, shows that with 50% of the data, the model contains 90% of targets, Adding more data adds a negligible increase in the percentage of targets included in the model.Gain/lift chartLift charts are often shown as a cumulative lift chart, which is also known as a gains chart. Therefore, gains charts are sometimes (perhaps confusingly) called “lift charts”, but they are more accurately cumulative lift charts.It is one of their most common uses is in marketing, to decide if a prospective client is worth calling.Gini CoefficientThe Gini coefficient or Gini Index is a popular metric for imbalanced class values. The coefficient ranges from 0 to 1 where 0 represents perfect equality and 1 represents perfect inequality. Here, if the value of an index is higher, then the data will be more dispersed.Gini coefficient can be computed from the area under the ROC curve using the following formula:Gini Coefficient = (2 * ROC_curve) — 1ConclusionUnderstanding how well a machine learning model is going to perform on unseen data is the ultimate purpose behind working with these evaluation metrics. Metrics like accuracy, precision, recall are good ways to evaluate classification models for balanced datasets, but if the data is imbalanced and there’s a class disparity, then other methods like ROC/AUC, Gini coefficient perform better in evaluating the model performance.Well, this concludes this article. I hope you guys have enjoyed reading it, feel free to share your comments/thoughts/feedback in the comment section.Thanks for reading !!!
Apr 06, 2021
In our fast-paced digital world, we're producing staggering volumes of data every day. This data falls into two key categories: structured, known for its order and efficiency, and unstructured, a captivating puzzle brimming with untapped potential.In this article, we will uncover how AI confronts the complexities of unstructured data, the hurdles it faces, and the intriguing opportunities it opens up to businesses from any kind of industry.Understanding Unstructured DataUnstructured data mining is the technique of extracting valuable and meaningful insights from an abundant well of unstructured data. It uncovers hidden gems of knowledge, making it a crucial pursuit in our data-rich era.In today's digital realm, unstructured data is generated in unprecedented quantities. Billions of text documents, images, and videos come to life daily, creating a treasure trove of information just waiting for organizations to explore.Unlocking the insights hidden within unstructured data can provide organizations with a competitive edge. This data can reveal customer sentiments, emerging trends, and valuable feedback that might otherwise go unnoticed.The Basics of Data MiningHow data mining works is that it discovers patterns, trends, and valuable information within a dataset. It involves various techniques to extract knowledge from raw data. While it's exceptionally effective with structured data, applying data mining to unstructured data requires a unique set of skills and tools.Unstructured Data MiningUnstructured data mining is a method focused on the extraction of valuable information from the vast, unstructured data available. This process uncovers hidden insights, making it a valuable endeavor in today's data-driven world.The AI RevolutionThe AI revolution has given rise to an exciting era of possibilities in unstructured data mining. AI's remarkable capabilities are instrumental in taming the unstructured data landscape, and it involves a multitude of components, including:Machine learning enables AI systems to learn from data, make predictions, and identify patterns, enhancing data mining capabilities.Deep learning uses neural networks to model complex patterns in unstructured data, which is particularly valuable in image and speech recognition.Sentiment analysis gauges emotional tones within textual data, helping to understand public opinion and tailor strategies.Pattern recognition identifies recurring structures in data, aiding in image processing and text mining.Knowledge graphs structure data relationships, improving contextual understanding and data retrieval.Anomaly detection identifies outliers in data, which is essential for fraud detection and data security.Challenges in Unstructured Data MiningAs promising as AI is at handling unstructured data, it's not without its set of challenges. Here, we delve into some of the major hurdles:Data QualityUnstructured data is inherently messy. It's laden with errors, inconsistencies, and biases, which makes it a challenge to extract meaningful insights from this data. AI systems need to be trained rigorously to navigate and decipher this diversity in data quality. Techniques like data cleansing, normalization, and the use of context are essential in ensuring that AI systems provide accurate results.ScalabilityAs the volume of unstructured data grows, AI systems must scale to handle the data influx effectively. Traditional hardware and algorithms might not be sufficient to handle this data influx. Scalable infrastructure and distributed computing become crucial to ensuring that AI systems can process and analyze vast amounts of data efficiently.Privacy ConcernsMining unstructured data often raises ethical questions regarding privacy and data protection. That’s why it’s essential to strike the right balance between data utilization and respecting individual privacy. It's a challenge to ensure that AI systems are used responsibly and in compliance with data protection laws and regulations, such as GDPR in Europe. Techniques like anonymization and consent management play a vital role in addressing these privacy concerns.Opportunities and ApplicationsAI's role in unstructured data mining has opened up a world of opportunities across various industries. Let's explore some of the most promising applications:Customer InsightsUnstructured data, particularly sourced from social media and customer reviews, serves as a goldmine of information on customer behavior and preferences. By leveraging AI algorithms, companies can analyze sentiments, spot emerging trends, and even forecast future buying patterns. With these insights, they can fine-tune their marketing strategies, product development, and customer service to align with their ever-evolving audience's demands.Healthcare DiagnosisThe abundance of unstructured data found in medical records, radiological images, and wearable device data holds the key to transformative advancements. AI-powered systems, known for their proficiency in the analysis of this data, not only facilitate early disease detection but also provide highly individualized treatment plans, ultimately raising the standard of patient care. For example: AI expedites the process of analyzing medical images for anomalies, resulting in a significant reduction in the time required for diagnosing and treating severe conditions.Fraud DetectionWhen it comes to financial institutions, AI is a vital tool for exposing fraudulent activities that often hide within the vast volumes of unstructured transaction data. Through a meticulous examination of transaction patterns and anomalies, AI systems can rapidly pinpoint fraudulent actions, providing businesses with a robust defense against significant financial losses. The ability to detect and thwart fraud in real-time provides a critical advantage, resulting in annual savings of billions of dollars for businesses.ConclusionThe future belongs to those who embrace the AI revolution in unstructured data mining. In this future, data isn't just information; it's the key to success. So, let's move forward, embracing this tomorrow, where possibilities are limitless and opportunities are endless.
Apr 06, 2021
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