Machine Learning Interview Questions and Answers Data Science

Below are different types of missing values can occur while the data collection process.

1. Missing values completely at random - If the probability of missing variable is the same across all observations, then it falls into this category. For example students determine that they will declare their preference whether to go to a cultural festival or not after tossing a fair coin. If a head occurs, then will declare that they will either go or do not decide to go and vice versa. Each observation has an equal chance of missing value whether to go or not go.
2. Missing values at random - This is different than “a” mentioned above. If the variable is missing at random and the missing ratio differs for different values of input variables, then this scenario occurs. For example: in a fair coin example setup, we have information of a set of people in a locality about their demographics, age, sex, locality type - busy/very busy/moderate busy, etc and if a female has a higher missing value of other parameters compared to male.
3. The missing value that depends on unobserved predictors - This case is possible when missing values are not completely at random. The phenomenon is based on unobserved input variable. Let’s say for example there is a mathematics examination and because of the complex level of examination, the expectation is that there will be fewer students who will go and appear the exam. Out of 100 students, 30 do not appear because of the “complexity level” of examination. This type of missing value is not at random. Instead, this is due to “complexity level” unless this parameter is not taken into account as a cause already.
4. The missing value which depends on missing value itself - This is a scenario when the probability of a missing value is correlated with the missing value itself. For example Students with higher or lower marks in graded exam in one subject are likely to appear/disappear in competitive exam for the same subject for another purpose/competition.

When a particular variable is missing in an observation or row, then we delete an entire row. This is called List wise deletion.

When the analysis is performed with all cases of a variable and then only those variable instances are deleted and not the entire row. This is called Pairwise deletion. This works like a correlation matrix.

Generally, pairwise deletion is preferred over listwise deletion as listwise deletion removes the entire row for a particular missing variable.

It is one of the methods to treat missing values other than direct deletion, imputation using a mean/median/mode value, etc. In kNN imputation, the missing values of an attribute are imputed using the given number of attributes that are most similar to the attribute whose values are missing. The similarity of two attributes is determined using a distance function. Pros and Cons are described below.

Outliers can have a significant impact based on the results of the data analysis and statistical modeling. These are as follows:

• Outliers can decrease normality as they are non-randomly distributed
• Error variance increases with a relative comparison and that provides an incorrect estimate of the overall population.
• Power of statistical tests are also reduced because of the impact in standard deviation.
• ANOVA, different relevant statistical model assumptions are impacted.

Here is an example with a sample dataset.

If we look at above, inclusion of an outlier shows huge difference in mean / average and standard deviation parameters.

There are various methods.

1. The most common method is to use visualization using box-plots, histograms and scatter plots to detect outliers.
2. Another way - Any value, which is beyond the range of -1.5 x IQR to 1.5 x IQR (where IQR stands for Inter-Quartile Range).
3. Use capping methods. Any value which out of range of 5th and 95th percentile can be considered an outlier.

Others could be as follows: Data points, three or more standard deviations away from the mean are considered as outlier.

There could be many assumptions. Five of them are described below:

1. The regression model is linear in parameters.
2. The mean of residuals is zero.
3. Homoscedasticity of residuals or equal variance.
4. No autocorrelations of residuals.
5. No perfect multicollinearity i.e. no perfect linear relationship between explanatory variables

A stationary time series has the following characteristics:

1. Mean or average is constant over time
2. Variance is constant over time
3. Autocorrelation is constant over time
4. Seasonality component may not have much impact over time

This type of time series is typically easy to predict as there not much variations expected in the pattern and trend.

Autocorrelation and partial autocorrelation are a type of measures of association between current time series and past time series values. Both of these provide an indication that older time series values are more useful in predicting future values.

Autocorrelation is the correlation of a Time Series with lags of itself. This is a significant metric because:

1. It is able to demonstrate the difference between a past state of time series observations and current state of time series observations and how much of lag impact. In below diagram time series of “Air Passengers” dataset is considered and ACF plot is drawn. As ACF lines are consistently outside of the dotted line, it indicates a significant correlation of lags in the series.
2. It also provides the aspect that the series is stationary or not. Autocorrelation plot is also called correlogram. If there is a stationary element, then correlogram will fall to zero, else if there is no stationary element, then correlogram will fall gradually slowly.

While comparing current time series steps to that of prior time series steps, there can be direct and indirect correlations. The indirect correlations are a linear function of correlation of the observation. There could be intervening time series steps. PACF or Partial autocorrelation tries to remove the effect of correlation due to shorter lags.

Both ACF and PACF are useful while trying to understand which model approach could be a relevant and better fit for a prediction solution.

Linear regression can be used to model the Time Series data with linear indices (Ex: 1, 2,...n). The resulting model’s residuals are a representation of the time series devoid of the trend.

In case, if some trend is left over to be seen in the residuals (like what it seems to be with ‘Figure1’ with myData below as an example), then you might wish to add few predictors to the lm() call (like a forecast:: seasonal dummy, forecast::Fourier or may be a lag of the series itself), until the trend is filtered.

Code snippet:

trModel <- lm(myData ~ c(1:length(myData)))
plot(resid(trModel), type="l")  # resid(trModel) contains the de-trended series

We can use the Augmented Dickey-Fuller Test (adf test) to test “stationary” aspect. A p-Value of less than 0.05 in adf.test() indicates that it is stationary.

Illustrative code snippet:

library(tseries)
adf.test(myData) # p-value < 0.05 indicates the TS is stationary kpss.test(myData)

It is a statistical test used to compare two related and matched samples. If a population can not be assumed to be normally distributed, then this test may be useful with the assumption that data are paired and from the same population. Each data pair is chosen randomly. It tries to compare between sample median and hypothetical median.

The boxplot below in R with the “air quality” sample data demonstrates the interpretation of the analysis using this test.

• boxplot(Ozone ~ Month, data = airquality)
• wilcox.test(Ozone ~ Month, data = airquality, subset = Month %in% c(5, 8))
• Wilcoxon rank sum test with continuity correction
• data: Ozone by Month
• W = 127.5, p-value = 0.0001208
• alternative hypothesis: true location shift is not equal to 0 Interpretation is this:
• If p-Value < 0.05, reject the null hypothesis and accept the alternative mentioned in your R code’s output.

Kolmogorov-Smirnov test is used to check whether 2 samples follow the same distribution.

• x <- rnorm(50)
• y <- runif(50)
• ks.test(x, y)

Two-sample Kolmogorov-Smirnov test

data: x and y

D = 0.52, p-value = 1.581e-06

alternative hypothesis: two-sided

• x <- rnorm(50)
• y <- rnorm(50)
• ks.test(x, y)

Two-sample Kolmogorov-Smirnov test

data: x and y

D = 0.1, p-value = 0.9667

alternative hypothesis: two-sided

If p-Value < 0.05 (significance level), we reject the null hypothesis that they are drawn from the same distribution. In other words, p < 0.05 implies x and y from different distributions.

Jitter plot is used for correlation. It provides pretty much all points which scatter plots typically do not show up.

We consider mpg dataset with city mileage (cty) and highway mileage (hwy). The original data has 234 data points but a typical scatter plot seems to display fewer points.

This is because there are many overlapping points appearing as a single dot. The fact that both cty and hwy are integers in the source dataset made it all the more convenient to hide this detail.

• load package and data library(ggplot2)

data(mpg, package="ggplot2") theme_set(theme_bw())

g <- ggplot(mpg, aes(cty, hwy))

• Scatterplot

g + geom_point() +

geom_smooth(method="lm", se=F) +

labs(subtitle="mpg: city vs highway mileage",

y="hwy",

x="cty",

title="Scatterplot with overlapping points",

caption="Source: midwest")

Now we can handle this with a Jitter plot.

We can make a jitter plot with jitter_geom(). As the name suggests, the overlapping points are randomly jittered around its original position based on a threshold controlled by

the width argument.

• load package and data library(ggplot2)

data(mpg, package="ggplot2")

• Jitter plot

theme_set(theme_bw()) # pre-set the bw theme.

g <- ggplot(mpg, aes(cty, hwy))

g + geom_jitter(width = .5, size=1) + labs(subtitle="mpg: city vs highway mileage",

y="hwy",

x="cty",

title="Jittered Points")

There are three types of error in any machine learning approach. They are a biased error, variance error, and irreducible error. Generally, the focus is to look at striking a balance between bias and variance and reducing those errors in the model so that accuracy can be improved.

Low Bias - indicates fewer assumptions about the form of the target variable or function. In this case, when we test on new data, it does not give expected results and accuracy can be compromised.

High variance - indicates large changes to the estimate of target variable or target function with changes to the training data.

It is always tricky to handle scenario to balance between these two as increasing the bias will decrease the variance and increasing the variance will decrease the bias. Hence approach that can be followed are as follows:

1. Look at the dataset in hand and contextual information to suggest which way to look at for a better prediction performance
2. Typically kNN and SVM algorithms can be looked at depending on what problem we are solving and how tweaks can be performed in order to manage this effect

This can be described in the below table.

For example, let’s consider a dataset of football players, their positions, their measurements, etc. We want to assign a position to these players in a new dataset which is unseen by the model which is learned using earlier training data. We may use kNN algorithm since there are measurements, but no positions are known. At the same time, let’s say we have another scenario where we have a dataset of these football players who are to be grouped into some specific groups based on some similarity between them. In this case, k-means could be used. So, both of these are context specific to the problem we are trying to solve.