Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

An overview of the self-organizing map algorithm, on which the papers in this issue are based, is presented in this article.

The Self-Organizing Map

How can we explain the predictions of a black-box model? In this paper, we use influence functions -- a classic technique from robust statistics -- to trace a model's prediction through the learning algorithm and back to its training data, thereby identifying training points most responsible for a given prediction. To scale up influence functions to modern machine learning settings, we develop a simple, efficient implementation that requires only oracle access to gradients and Hessian-vector products. We show that even on non-convex and non-differentiable models where the theory breaks down, approximations to influence functions can still provide valuable information. On linear models and convolutional neural networks, we demonstrate that influence functions are useful for multiple purposes: understanding model behavior, debugging models, detecting dataset errors, and even creating visually-indistinguishable training-set attacks.

Understanding Black-box Predictions via Influence Functions

How can we explain the predictions of a black-box model? In this paper, we use influence functions — a classic technique from robust statistics — to trace a model's prediction through the learning algorithm and back to its training data, thereby identifying training points most responsible for a given prediction. To scale up influence functions to modern machine learning settings, we develop a simple, efficient implementation that requires only oracle access to gradients and Hessian-vector products. We show that even on non-convex and non-differentiable models where the theory breaks down, approximations to influence functions can still provide valuable information. On linear models and convolutional neural networks, we demonstrate that influence functions are useful for multiple purposes: understanding model behavior, debugging models, detecting dataset errors, and even creating visually-indistinguishable training-set attacks.

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Understanding black-box predictions via influence functions

Model selection is one of the key issues both in recent research and application of kernel methods. Cross-validation is a commonly employed and widely accepted model selection criterion. However, it requires multiple times of training the algorithm under consideration, which is computationally intensive. In this paper, we present a novel strategy for approximating the cross-validation based on the Bouligand influence function (BIF), which only requires the solution of the algorithm once. The BIF measures the impact of an infinitesimal small amount of contamination of the original distribution. We first establish the link between the concept of BIF and the concept of cross-validation. The BIF is related to the first order term of a Taylor expansion. Then, we calculate the BIF and higher order BIFs, and apply these theoretical results to approximate the cross-validation error in practice. Experimental results demonstrate that our approximate cross-validation criterion is sound and efficient.

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Efficient Approximation of Cross-Validation for Kernel Methods using Bouligand Influence Function

Meta-ELM: ELM with ELM hidden nodes

Cross-validation (CV) is a widely adopted approach for selecting the optimal model. However, the computation of empirical cross-validation error (CVE) has high complexity due to multiple times of learner training. In this paper, we develop a novel approximation theory of CVE and present an approximate approach to CV based on the Bouligand influence function (BIF) for kernel-based algorithms. We first represent the BIF and higher order BIFs in Taylor expansions, and approximate CV via the Taylor expansions. We then derive an upper bound of the discrepancy between the original and approximate CV. Furthermore, we provide a novel computing method to calculate the BIF for general distribution, and evaluate BIF criterion for sample distribution to approximate CV. The proposed approximate CV requires training on the full data set only once and is suitable for a wide variety of kernel-based algorithms. Experimental results demonstrate that the proposed approximate CV is sound and effective.

Fast Cross-Validation for Kernel-Based Algorithms

Granularity selection for cross-validation of SVM

Kernel learning is a fundamental problem both in recent research and application of kernel methods. Existing kernel learning methods commonly use some measures of generalization errors to learn the optimal kernel in a convex (or conic) combination of prescribed basic kernels. However, the generalization bounds derived by these measures usually have slow convergence rates, and the basic kernels are finite and should be specified in advance. In this paper, we propose a new kernel learning method based on a novel measure of generalization error, called principal eigenvalue proportion (PEP), which can learn the optimal kernel with sharp generalization bounds over the convex hull of a possibly infinite set of basic kernels. We first derive sharp generalization bounds based on the PEP measure. Then we design two kernel learning algorithms for finite kernels and infinite kernels respectively, in which the derived sharp generalization bounds are exploited to guarantee faster convergence rates, moreover, basic kernels can be learned automatically for infinite kernel learning instead of being prescribed in advance. Theoretical analysis and empirical results demonstrate that the proposed kernel learning method outperforms the state-of-the-art kernel learning methods.

Shizhong Liao

Papers

Efficient Approximation of Cross-Validation for Kernel Methods using Bouligand Influence Function

Meta-ELM: ELM with ELM hidden nodes

Fast Cross-Validation for Kernel-Based Algorithms

Granularity selection for cross-validation of SVM

Infinite Kernel Learning: Generalization Bounds and Algorithms.