Demo Quiz – Self Preparation

140 like tea while 80 like both tea and coffee. So 60 like only tea. 120 like coffee and  80 like both tea and coffee, so 40 like only coffee. Then 60 + 40 + 80 = 180 like either tea or coffee. 

The naive Baye’s classifier makes the naive assumption that  various feature dimensions are independent conditioned on the class .

Naive Bayes classifier : Suppose you have M dimensional data of the form and you want to predict the class for this data. From Bayes rule we have : 

Using the naive Baye’s assumption of independence of all features  given y, we can write :

Matrix multiplication is associative, i.e. (AB)C = A(BC)
Matrix multiplication is distributive, i.e. A(B+C) = AB+AC
Matrix multiplication may not be commutative, i.e. AB = BA only if m=q in the given case

For convex functions, f”(x) >= 0 for any x is the sufficient condition for local minimum. So it doesn’t matter if x is zero or not, f”(x) has to be non negative for f(x) to have local minimum, at point x where f'(x) is 0.

For any Machine Learning task in hand, we need to first give some time to understand the problem. Sometimes it is done with the help of domain experts. Once the problem has been understood, we need to check if it is a supervised or unsupervised learning problem. This can be determined by knowing what is the desired goal and whether we have labels or not. Once we know if its a clustering or classification problem, we do the train test split for better generalization. In most cases it is train-validation-test split but for simplicity we kept train-test split. Notice that train-test split happens before the data preprocessing as we don’t want test data to be used in preprocessing for better generalization. Whatever preprocessing is applied(sklearn’s fit function) on training data, test data is transformed similarly(using sklearn’s transform function). Post train-test split , we select the right features and then pre-process the data by scaling, normalization, replacing missing values in the features and other required processing in this step. And then lastly, we select the right model. Note that model selection would also include the task of determining what loss function to use.

If each point belongs to a different cluster then that point becomes the cluster centre by triviality. Error in K-Means algorithm is calculated by taking the sum of squared distances of instances between their cluster centres, also called inertia. If K = N, there are N clusters and each point is its cluster centre. Hence the error becomes 0 which is the minimum possible error.

Don’t worry about the points if its showing incorrect answer.
If the application doesn’t use any user inputs directly in the application, most likely it is based on unsupervised learning. User inputs act as supervision in many applications but in some it might just be data and not the labels.

DBSCAN is a density based clustering algorithm. It separates high density regions from low density regions using params like epsilon and minPoints. Epsilon takes care of the closeness between the points in the same cluster. minPoints ensure lower density regions do not form any clusters. This makes it more robust to outliers instead of sensitive to outliers(noise). Due to these params, it does not perform well for varying density clusters as epsilon and minPoints parameters are fixed for all density clusters.

This follows from the following equation in n-dimensions

Using the fact that the above function is convex function and hence first order condition is necessary and sufficient. Taking the first derivative and equating it to zero to find

Please refer to this link for detailed explanation on Linear Regression.

Logistic regression is linear not because of sigmoid function but due to linearity in parameters. Sigmoid function, on the other hand, is a nonlinear function used to convert a real number to a number between 0 and 1.