Databricks-Certified-Professional-Data-Scientist Databricks Certified Professional Data Scientist Exam Questions and Answers

Error calculation allows you to see how well a machine learning

method is performing.

One way of determining this performance is to calculate a numerical error This number is sometimes a percent,

however it can also be a score or distance. The goal is usually to minimize an error

percent or distance :

however th goal may be to minimize or maximize a score. Encog supports the

following error calculation methods.

Sum of Squares Error (ESS)

Root Mean Square Error (RMS)

Mean Square Error (MSE) (default)

SOM Error (Euclidean Distance Error)

RMSE measures error of a predicted numeric value, and so applies to contexts like

regression and some recommender system techniques,

which rely on predicting a numeric value. It is not relevant to classification

techniques

like logistic regression and Naive Bayes, which predict categorical values.

It also is not relevant to unsupervied techniques like clustering.

The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) is a

frequently used measure of the

differences between values predicted by a model or an estimator and the values

actually observed. Basically,

the RMSD represents the sample standard deviation of the differences between

predicted values and observed values.

These individual differences are called residuals when the calculations are

performed over the data sample that was used for estimation,

and are called prediction errors when computed out-of-sample. The RMSD serves

to aggregate the magnitudes

of the errors in predictions for various times into a single measure of predictive

power. RMSD is a good measure of accuracy,

but only to compare forecasting errors of different models for a particular variable

and not between variables, as it is scale-dependent.

If you re trying to predict or forecast a target value, then you need to look into supervised learning. If not, then unsupervised learning is the place you want to be. If you ' ve chosen supervised learning, what ' s your target value? Is it a discrete value like Yes/No, 1/2/3, A/B/C : or Red/Yellow/Black? If so, then you want to look into classification. If the target value can take on a number of values, say any value from 0.00 to 100.00, or-999 to 999, or+_to -_, then you need to look into regression. If you ' re not trying to predict a target value : then you need to look into unsupervised learning. Are you trying to fit your data into some discrete groups? If so and that ' s all you need, you should look into clustering. Do you need to have some numerical estimate of how strong the fit is into each group? If you answer yes then you probably should look into a density estimation algorithm.

Since 10 out of 100 students are both French and female, then

P(AandB)=10100

Also. 60 out of the 100 students are French, so

P(B)=60100

So the required probability is:

P(A|B)=P(AandB)P(B)=10/10060/100=16

The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) is a frequently used measure of the differences between values predicted by a model or an estimator and the values actually observed. Basically, the RMSD represents the sample standard deviation of the differences between predicted values and observed values. These individual differences are called residuals when the calculations are performed over the data sample that was used for estimation, and are called prediction errors when computed out-of-sample. The RMSD serves to aggregate the magnitudes of the errors in predictions for various times into a single measure of predictive power. RMSD is a good measure of accuracy, but only to compare forecasting errors of different models for a particular variable and not between variables, as it is scale-dependent. RMSE is calculated as the square root of the mean of the squares of the errors. The error in every case in this example is 1. The square of 1 is 1 The average of n items with value 1 is 1 The square root of 1 is 1 The RMSE is therefore 1

Logistic regression is used widely in many fields, including the medical and social sciences. For example, the Trauma and Injury Severity Score (TRISS), which is widely used to predict mortality in injured patients, was originally developed by Boyd et al. using logistic regression. Many other medical scales used to assess severity of a patient have been developed using logistic regression. Logistic regression may be used to predict whether a patient has a given disease (e.g. diabetes; coronary heart disease), based on observed characteristics of the patient (age, sex, body mass index, results of various blood tests, etc.; age, blood cholesterol level, systolic blood pressure, relative weight, blood hemoglobin level, smoking (at 3 levels), and abnormal electrocardiogram.).Another example might be to predict whether an American voter will vote Democratic or Republican, based on age, income, sex, race, state of residence, votes in previous elections, etc. The technique can also be used in engineering, especially for predicting the probability of failure of a given process, system or product. It is also used in marketing applications such as prediction of a customer ' s propensity to purchase a product or halt a subscription, etc.[citation needed] In economics it can be used to predict the likelihood of a person ' s choosing to be in the labor force, and a business application would be to predict the likelihood of a homeowner defaulting on a mortgage. Conditional random fields, an extension of logistic regression to sequential data, are used in natural language processing.

Principal component analysis (PCA) involves a mathematical procedure that transforms a number of (possibly) correlated variables into a (smaller) number of uncorrelated variables called principal components. The first principal component accounts for as much of the variability in the data as possible: and each succeeding component accounts for as much of the remaining variability as possible.

Objectives of principal component analysis

1. To discover or to reduce the dimensionality of the data set.

2. To identify new meaningful underlying variables.

The marginal probability P(H=Hit) is the sum along the H=Hit row of this joint distribution table, as this is the probability of being hit when the lights are red OR yellow OR green. Similarly, the marginal probability that P(H=Not Hit) is the sum of the H=Not Hit row

Explanation : k-Nearest Neighbors

Pros: High accuracy insensitive to outliers, no assumptions about data

Cons: Computationally expensive, requires a lot of memory

Works with: Numeric values, nominal values

Explanation : The RMSE serves to aggregate the magnitudes of the errors in predictions for various times into a single measure of predictive power. RMSE is a good measure of accuracy, but only to compare forecasting errors of different models for a particular variable and not between variables, as it is scale-dependent.

This is the standard solution of the normal equations for linear regression. Because A is not square, you cannot simply take its inverse.

There is a tradeoff between cost and stability in unsupervised learning. The more tightly you fit the data, the less stable the model will be, and vice versa. The idea is to find a good balance with more weight given to the cost. Typically a good approach is to set a stability threshold and select the model that achieves the lowest cost above the stability threshold.

To see how this is done, let W represent the event that the conversation was held with a woman, and L denote the event that the conversation was held with a long ­haired person. It can be assumed that women constitute half the population for this example. So, not knowing anything else, the probability that W occurs is P(W) = 0.5. Suppose it is also known that 75% of women have long hair which we denote as P(L |W) = 0.75 (read: the probability of event L given event W is 0.75, meaning that the probability of a person having long hair (event " L " ) : given that we already know that the person is a woman ( " event W " ) is 75%). Likewise, suppose it is known that 15% of men have long hair, or P(L |M) = 0.15; where M is the complementary event of W : i.e. ; the event that the conversation was held with a man (assuming that every human is either a man or a woman).

Our goal is to calculate the probability that the conversation was held with a woman, given the fact that the person had long hair, or, in our notation, P(W |L). Using the formula for Bayes ' theorem, we have:

Text Description automatically generated with low confidence

where we have used the law of total probability to expand

P(L),

The numeric answer can be obtained by substituting the above values into this formula (the algebraic multiplication is annotated using " * " , the centered dot). This yields

A picture containing table Description automatically generated

i.e., the probability that the conversation was held with a woman, given that the person had long hair is about 83%. More examples are provided below.

Linear regression models a linear relationship of a scalar dependent variable y to one or more explanatory independent variables x to build a model of coefficients.

Bayes ' theorem (also known as Bayes ' rule) is a useful tool for calculating conditional probabilities.

Explanation : Logistic regression

Pros: Computationally inexpensive, easy to implement, knowledge representation

easy to interpret

Cons: Prone to underfitting, may have low accuracy Works with: Numeric values, nominal values

Classification : Build models to classify data into different categories credit scoring, tumor detection, image recognition Regression: Build models to predict continuous data, electricity load forecasting, algorithmic trading, drug discovery

The two most common regularization methods are called L1 and L2 regularization. L1 regularization penalizes the weight vector for its L1-norm (i.e. the sum of the absolute values of the weights), whereas L2 regularization uses its L2-norm. There is usually not a considerable difference between the two methods in terms of the accuracy of the resulting model (Gao et al 2007), but L1 regularization has a significant advantage in practice. Because many of the weights of the features become zero as a result of L1-regularized training, the size of the model can be much smaller than that produced by L2-regularization. Compact models require less space on memory and storage, and enable the application to start up quickly. These merits can be of vital importance when the application is deployed in resource-tight environments such as cell-phones.

Regularization works by adding the penalty associated with the coefficient values to the error of the hypothesis. This way, an accurate hypothesis with unlikely coefficients would be penalized whila a somewhat less accurate but more conservative hypothesis with low coefficients would not be penalized as much.

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Logistic regression is a model used for prediction of the probability of occurrence of an event. It makes use of several predictor variables that may be either numerical or categories.

We address two cases of the target variable. The first case occurs when the target variable can take only nominal values: true or false; reptile, fish: mammal, amphibian, plant, fungi. The second case of classification occurs when the target variable can take an infinite number of numeric values, such as 0.100, 42.001, 1000.743, .... This case is called regression.

The sample space is defined by two mutually-exclusive events - it rains or it does not rain. Additionally, a third event occurs when the weatherman predicts rain. You should consider Bayes ' theorem when the following conditions exist.

• The sample space is partitioned into a set of mutually exclusive events {A1, A2,... : An}.

• Within the sample space, there exists an event B : for which P(B) > 0.

• The analytical goal is to compute a conditional probability of the form: P( Ak B).

The method based on principal component analysis (PCA) evaluates the features according to the projection of the largest eigenvector of the correlation matrix on the initial dimensions, the method based on Fisher ' s linear discriminant analysis evaluates. Them according to the magnitude of the components of the discriminant vector.

The first principal component corresponds to the greatest variance in the data, by definition. If we project the data onto the first principal component line, the data is more spread out (higher variance) than if projected onto any other line, including other principal components.

In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variable) denoted X. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression. (This term should be distinguished from multivariate linear regression^ where multiple correlated dependent variables are predicted, rather than a single scalar variable.) In linear regression data are modeled using linear predictor functions, and unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, linear regression refers to a model in which the conditional mean of y given the value of X is an affine function of X. Less commonly : linear regression could refer to a model in which the median, or some other quantile of the conditional distribution of y given X is expressed as a linear function of X. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of y given X, rather than on the joint probability distribution of y and X : which is the domain of multivariate analysis.

Logistic regression is widely used in machine learning for classification problems. It is well-known that regularization is required to avoid over-fitting, especially when there is a only small number of training examples, or when there are a large number of parameters to be learned. In particular L1 regularized logistic regression is often used for feature selection, and has been shown to have good generalization performance in the presence of many irrelevant features. (Ng 2004; Goodman 2004) Unregularized logistic regression is an unconstrained convex optimization problem with a continuously differentiate objective function. As a consequence, it can be solved fairly efficiently with standard convex optimization methods, such as Newton ' s method or conjugate gradient. However, adding the L1 regularization makes the optimization

problem com-putationally more expensive to solve. If the L1 regulariza-tion is enforced by an L1 norm constraint on the parameLogistic regression is a classifier and L1 regularization tends to produce models that ignore dimensions of the input that are not predictive. This is particularly useful when the input contains many dimensions, k-nearest neighbors classification is also a classification technique, but relies on notions of distance. In a high-dimensional space, most every data point is " far " from others (the curse of dimensionality) and so these techniques break down. Naive Bayes is not inherently regularizing. Random forests represent an ensemble method; but an ensemble method is not necessarily more suitable to high-dimensional data. Practically, I think the biggest reasons for regularization are 1) to avoid overfitting by not generating high coefficients for predictors that are sparse. 2) to stabilize the estimates especially when there ' s collinearity in the data.

1) is inherent in the regularization framework. Since there are two forces pulling each other in the objective function, if there ' s no meaningful loss reduction, the increased penalty from the regularization term wouldn ' t improve the overall objective function. This is a great property since a lot of noise would be automatically filtered out from the model. To give you an example for 2), if you have two predictors that have same values, if you just run a regression algorithm on it since the data matrix is singular your beta coefficients will be Inf if you try to do a straight matrix inversion. But if you add a very small regularization lambda to it, you will get stable beta coefficients with the coefficient values evenly divided between the equivalent two variables. For the difference between L1 and L2, the following graph demonstrates why people bother to have L1 since L2 has such an elegant analytical solution and is so computationally straightforward. Regularized regression can also be represented as a constrained regression problem (since they are Lagrangian equivalent). The implication of this is that the L1 regularization gives you sparse estimates. Namely, in a high dimensional space, you got mostly zeros and a small number of non-zero coefficients. This is huge since it incorporates variable selection to the modeling problem. In addition, if you have to score a large sample with your model, you can have a lot of computational savings since you don ' t have to compute features(predictors) whose coefficient is 0. I personally think L1 regularization is one of the most beautiful things in machine learning and convex optimization. It is indeed widely used in bioinformatics and large scale machine learning for companies like Facebook, Yahoo, Google and Microsoft.

Principal component analysis . or PCA, is a technique for taking a dataset that is in the form of a set of tuples representing points in a high-dimensional space and finding the dimensions along which the tuples line up best. The idea is to treat the set of tuples as a matrix M and find the eigenvectors for MMT or M T M . The matrix of these eigenvectors can be thought of as a rigid rotation in a high-dimensional space. When you apply this transformation to the original data, the axis corresponding to the principal eigenvector is the one along which the points are most " spread out, 11 More precisely this axis is the one along which the variance of the data is maximized. Put another way, the points can best be viewed as lying along this axis, with small deviations from this axis.

Correlation measures the linear relationship (Pearson ' s correlation) or monotonic relationship (Spearman ' s correlation) between two variables, X and Y. Mutual information is more general and measures the reduction of uncertainty in Y after observing X. It is the KL distance between the joint density and the product of the individual densities. So Ml can measure non-monotonic relationships and other more complicated relationships

Mutual information is a quantification of the dependency between random variables. It is sometimes contrasted with linear correlation since mutual information captures nonlinear dependence.

Features with high mutual information with the predicted value are good. However a feature may have high mutual information because it is highly correlated with another feature that has already been selected. Choosing another feature with somewhat less mutual information with the predicted value, but low mutual information with other selected features, may be more beneficial. Hence it may help to also prefer features that are less redundant with other selected features.

1 Collect data. You could collect the samples by scraping a website and extracting data : or you could get information from an RSS feed or an API. You could have a device collect wind speed measurements and send them to you, or blood glucose levels, or anything you can measure. The number of options is endless. To save some time and effort you could use publicly available data

2 Prepare the input data. Once you have this data, you need to make sure it ' s in a useable format. The format we ' ll be using in this book is the Python list. We ' ll talk about Python more in a little bit, and lists are reviewed in appendix A. The benefit of having this standard format is that you can mix and match algorithms and data sources. You may need to do some algorithm-specific formatting here. Some algorithms need features in a special format, some algorithms can deal with target variables and features as strings, and some need them to be integers. We ' ll get to this later but the algorithm-specific formatting is usually trivial compared to collecting data.

3 Analyze the input data. This is looking at the data from the previous task. This could be as simple as looking at the data you ' ve parsed in a text editor to make sure steps 1 and 2 are actually working and you don ' t have a bunch of empty values. You can also look at the data to see if you can recognize any patterns or if there ' s anything obvious^ such as a few data points that are vastly different from the rest of the set. Plotting data in one : two, or three dimensions can also help. But most of the time you ' ll have more than three features, and you can ' t easily plot the data across all features at one time. You could, however use some advanced methods we ' ll talk about later to distill multiple dimensions down to two or three so you can visualize the data.

4 If you ' re working with a production system and you know what the data should look like, or you trust its source : you can skip this step. This step takes human involvement, and for an automated system you don ' t want human involvement. The value of this step is that it makes you understand you don ' t have garbage coming in.

5 Train the algorithm. This is where the machine learning takes place. This step and the next step are where the " core " algorithms lie, depending on the algorithm.You feed the algorithm good clean data from the first two steps andextract knowledge or information. This knowledge you often store in a formatthat ' s readily useable by a machine for the next two steps.In the case of unsupervised learning, there ' s no training step because youdon ' t have a target value. Everything is used in the next step.

6 Test the algorithm. This is where the information learned in the previous step isput to use. When you ' re evaluating an algorithm, you ' ll test it to see how well itdoes. In the case of supervised learning, you have some known values you can use to evaluate the algorithm. In unsupervised learning, you may have to use some other metrics to evaluate the success. In either case, if you ' re not satisfied, you can go back to step 4, change some things, and try testing again. Often thecollection or preparation of the data may have been the problem, and you ' ll have to go back to step 1.

7 Use it. Here you make a real program to do some task, and once again you see if all the previous steps worked as you expected. You might encounter some new data and have to revisit steps 1-5.

Principal component analysis (PCA) involves a mathematical procedure that

transforms a number of (possibly) correlated variables into a

(smaller) number of uncorrected variables called principal components. The first

principal component accounts for as

much of the variability in the data as possible, and each succeeding component

accounts for as much of the remaining variability as possible.

An advantage of naive Bayes is that it only requires a small amount of training data to estimate the parameters (means and variances of the variables) necessary for classification. Because independent variables are assumed, only the variances of the variables for each class need to be determined and not the entire covariance matrix.