Statistical learning methods

Statistical learning methods are focused on supervised and unsupervised modeling and prediction. Statistical Learning Methods are used to estimate functions that connect inputs to outputs.  Most statistical learning methods can be characterised as either parametric or non-parametric.  Restrictive models are much more intepretable than flexible ones. Flexible approaches can be so complicated that it is hard to understand how predictors affect the response.  If inference is the goal, simple and inflexible methods are easier to interpret. For prediction, accuracy is the biggest concern. However, flexible models are more prone to overfitting.

The simplest AI applications can be divided into two types: classifiers (“if shiny then diamond”) and controllers (“if diamond then pick up”). Controllers do, however, also classify conditions before inferring actions, and therefore classification forms a central part of many AI systems. Classifiers are functions that use pattern matching to determine a closest match. They can be tuned according to examples, making them very attractive for use in AI.

These examples are known as observations or patterns. In supervised learning, each pattern belongs to a certain predefined class. A class is a decision that has to be made. All the observations combined with their class labels are known as a data set. When a new observation is received, that observation is classified based on previous experience.

statistical learning

A classifier can be trained in various ways; there are many statistical and machine learning approaches. The decision tree is the simplest and most widely used symbolic machine learning algorithm. K-nearest neighbour algorithm was the most widely used analogical AI until the mid-1990s. Kernel methods such as the support vector machine (SVM) displaced k-nearest neighbour in the 1990s. The naive Bayes classifier is reportedly the “most widely used learner” at Google, due in part to its scalability. Neural networks are also used for classification.

Classifier performance depends greatly on the characteristics of the data to be classified, such as the dataset size, distribution of samples across classes, the dimensionality, and the level of noise. Model-based classifiers perform well if the assumed model is an extremely good fit for the actual data. Otherwise, if no matching model is available, and if accuracy (rather than speed or scalability) is the sole concern, conventional wisdom is that discriminative classifiers (especially SVM) tend to be more accurate than model-based classifiers such as “naive Bayes” on most practical data sets.


Assessing Statistical Learning Models Accuracy

Every data set is different and there is no one statistical learning method that works best for all data sets. It is important for any given data set to find the statistical learning method that produces the best results. This section presents some concepts that are part of that decision-making process.


Statistical classification

In statistics, classification is the problem of identifying which of a set of categories (sub-populations) an observation (or observations) belongs to. Examples are assigning a given email to the “spam” or “non-spam” class, and assigning a diagnosis to a given patient based on observed characteristics of the patient (sex, blood pressure, presence or absence of certain symptoms, etc.).

Often, the individual observations are analyzed into a set of quantifiable properties, known variously as explanatory variables or features. These properties may variously be categorical (e.g. “A”, “B”, “AB” or “O”, for blood type), ordinal (e.g. “large”, “medium” or “small”), integer-valued (e.g. the number of occurrences of a particular word in an email) or real-valued (e.g. a measurement of blood pressure). Other classifiers work by comparing observations to previous observations by means of a similarity or distance function.

An algorithm that implements classification, especially in a concrete implementation, is known as a classifier. The term “classifier” sometimes also refers to the mathematical function, implemented by a classification algorithm, that maps input data to a category.

Terminology across fields is quite varied. In statistics, where classification is often done with logistic regression or a similar procedure, the properties of observations are termed explanatory variables (or independent variables, regressors, etc.), and the categories to be predicted are known as outcomes, which are considered to be possible values of the dependent variable.  In machine learning, the observations are often known as instances, the explanatory variables are termed features (grouped into a feature vector), and the possible categories to be predicted are classes. Other fields may use different terminology: e.g. in community ecology, the term “classification” normally refers to cluster analysis.


Relation to other problems

Classification and clustering are examples of the more general problem of pattern recognition, which is the assignment of some sort of output value to a given input value. Other examples are regression, which assigns a real-valued output to each input; sequence labeling, which assigns a class to each member of a sequence of values (for example, part of speech tagging, which assigns a part of speech to each word in an input sentence); parsing, which assigns a parse tree to an input sentence, describing the syntactic structure of the sentence; etc.

A common subclass of classification is probabilistic classification. Algorithms of this nature use statistical inference to find the best class for a given instance. Unlike other algorithms, which simply output a “best” class, probabilistic algorithms output a probability of the instance being a member of each of the possible classes. The best class is normally then selected as the one with the highest probability. However, such an algorithm has numerous advantages over non-probabilistic classifiers:

  • It can output a confidence value associated with its choice (in general, a classifier that can do this is known as a confidence-weighted classifier)
  • Correspondingly, it can abstain when its confidence of choosing any particular output is too low
  • Because of the probabilities which are generated, probabilistic classifiers can be more effectively incorporated into larger machine-learning tasks, in a way that partially or completely avoids the problem of error propagation.

Put more simply, Classification is a common scenario.

  1. Person arrives at ER exhibiting particular symptoms. What illness does he have?
  2. Money is wired to an external account at a bank. Is this fraud?
  3. Email is sent to your account. Is it legit, or spam?

Similar to regression, we have a set of training observations that use to build a classifier. We also want the classifier to perform well on both training and test observations.


Cluster analysis

Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of exploratory data analysis, and a common technique for statistical data analysis, used in many fields, including pattern recognition, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning.

Cluster analysis itself is not one specific algorithm, but the general task to be solved. It can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with small distances between cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering can therefore be formulated as a multi-objective optimisation problem.

The appropriate clustering algorithm and parameter settings (including parameters such as the distance function to use, a density threshold or the number of expected clusters) depend on the individual data set and intended use of the results. Cluster analysis as such is not an automatic task, but an iterative process of knowledge discovery or interactive multi-objective optimisation that involves trial and failure. It is often necessary to modify data preprocessing and model parameters until the result achieves the desired properties.

Besides the term clustering, there are a number of terms with similar meanings, including automatic classification, numerical taxonomy, botryology (from Greek βότρυς “grape”), typological analysis, and community detection. The subtle differences are often in the use of the results: while in data mining, the resulting groups are the matter of interest, in automatic classification the resulting discriminative power is of interest.


Statistical learning theory

Statistical learning theory is a framework for machine learning drawing from the fields of statistics and functional analysis. Statistical learning theory deals with the statistical inference problem of finding a predictive function based on data. Statistical learning theory has led to successful applications in fields such as computer vision, speech recognition, and bioinformatics.

The goals of learning are understanding and prediction. Learning falls into many categories, including supervised learning, unsupervised learning, online learning, and reinforcement learning. From the perspective of statistical learning theory, supervised learning is best understood.  Supervised learning involves learning from a training set of data. Every point in the training is an input-output pair, where the input maps to an output. The learning problem consists of inferring the function that maps between the input and the output, such that the learned function can be used to predict the output from future input.

Depending on the type of output, supervised learning problems are either problems of regression or problems of classification. If the output takes a continuous range of values, it is a regression problem. 

Classification problems are those for which the output will be an element from a discrete set of labels. Classification is very common for machine learning applications. In facial recognition, for instance, a picture of a person’s face would be the input, and the output label would be that person’s name. The input would be represented by a large multidimensional vector whose elements represent pixels in the picture.  After learning a function based on the training set data, that function is validated on a test set of data, data that did not appear in the training set.

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