Model Evaluation and Selection(Part-3)

 Hypothesis Testing


Given a hypothesis, test if it is true with a particular confidence 
• Hypotheses: errorD (h1) > errorD (h2) 
• What % of the probability mass is associated with errorD (h1) - errorD (h2) > 0 
• Example 
• Let the error rates measured for the two hypotheses h1 and h2 on a sample of size 100 be 0.3 and 0.2 respectively 
• The standard deviation for the normal distribution defined on d’ = errorS1 (h1 )- errorS2 (h2 ) is • 1.640.061 = 0.1 
• 1.64 standard deviation corresponds to the 90% confidence interval and hence the % mass of the probability distribution > 0 is 95% 
• Result: Accept the hypothesis with 95% confidence that h2 is a more accurate hypothesis than h1 on D (the underlying population)

Comparing Two Algorithms

Given two learning algorithms, L1 and L2 , which one is better, on average, at learning a particular target function 
• Estimating the relative performance 
• Calculate the Expected Value of the difference in errors 
• For all samples of size n, consider the relative performance of L1 and L2 
• Estimate the error over all training samples S of D ESD [errorD (L1 (S))- errorD (L2 (S))] 
• where L1 (S) and L2 (S) are the hypotheses generated by the learning algorithms from the sample S 
• Can be estimated by 
• Holding back part of the training data for testing 
• Using multiple samples of the training data D 
• Cross-validation 
• Bootstrapping

Cross-validation:
Cross-validation is a resampling procedure used to evaluate machine learning models on a limited data sample. The procedure has a single parameter called k that refers to the number of groups that a given data sample is to be split into. As such, the procedure is often called k-fold cross-validation.

Bootstraping
Sample, with replacement, the training data (of size N) and use the sample (of size N) to learn the model 
• The same instance in the training data can appear multiple times in the data used for learning the model 
• An instance within the training data may not appear at all in the data used for learning 
• Use remaining data as test data 
• Repeat multiple times to obtain an error estimate and a confidence interval.

Confusion Matrix 



• Contingency table containing information regarding the actual and predicted value of the class labels 

Comments

Post a Comment

Popular posts from this blog

Supervised Learning(Part-5)

Image
  Decision Trees (Continued) Attribute Selection Measures If the dataset consists of N attributes then deciding which attribute to place at the root or at different levels of the tree as internal nodes is a complicated step. By just randomly selecting any node to be the root can’t solve the issue. If we follow a random approach, it may give us bad results with low accuracy. For solving this attribute selection problem, researchers worked and devised some solutions. They suggested using some criteria like : Entropy, Information gain, Gini index, Gain Ratio, Reduction in Variance Chi-Square These criteria will calculate values for every attribute. The values are sorted, and attributes are placed in the tree by following the order i.e, the attribute with a high value(in case of information gain) is placed at the root. While using Information Gain as a criterion, we assume attributes to be categorical, and for the Gini index, attributes are assumed to be continuous. Entropy Entropy is a me
Read more

Supervised Learning(Part-2)

Image
  Support Vector Machine A Support Vector Machine (SVM) is a discriminative classifier formally defined by a separating hyperplane. In other words, given labeled training data, the algorithm outputs an optimal hyperplane which categorizes new examples.  In two dimensional space this hyperplane is a line dividing a plane in two parts where in each class lay in either side. Suppose given plot of two label classes on graph as shown in image. You might have come up with something similar to following image (image B). It fairly separates the two classes. Any point that is left of line falls into black circle class and on right falls into blue square   In real world application, finding perfect class for millions of training data set takes lot of time. This is called regularization parameter.  Two terms regularization parameter and gamma are tuning parameters in SVM classifier. Varying those we can achieve considerable non linear classification line with more accuracy in reasonable amount of
Read more

Text Analysis (Part - 4)

Image
  The article covers a very important concepts of Text Analysis from Bayesian's i.e the  Latent Dirichlet Allocation  which is the part of topic modelling . What is Topic Modelling? Topic modelling is a type of statistical modelling for discovering the abstract “topics” that occur in a collection of documents. This can be useful for search engines, customer service automation, and any other instance where knowing the topics of documents is important . Thus, Topic Models , in a nutshell, are a type of statistical language models used for uncovering hidden structure in a collection of texts. There are multiple methods of for topic modelling and one of them includes Latent Dirichlet Allocation (LDA) . Latent Dirichlet Allocation Latent Dirichlet Allocation (LDA) is an example of topic model and is used to classify text in a document to a particular topic. It builds a topic per document model and words per topic model, modelled as Dirichlet distributions. Basic Idea LDA is a  genera
Read more