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

Analytic Combinatorics is a self-contained treatment of the mathematics underlying the analysis of discrete structures, which has emerged over the past several decades as an essential tool in the understanding of properties of computer programs and scientific models with applications in physics, biology and chemistry. Thorough treatment of a large number of classical applications is an essential aspect of the presentation. Written by the leaders in the field of analytic combinatorics, this text is certain to become the definitive reference on the topic. The text is complemented with exercises, examples, appendices and notes to aid understanding therefore, it can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study.

Analytic Combinatorics

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

527 articles related to imbalanced data and rare events are reviewed.Viewing reviewed papers from both technical and practical perspectives.Summarizing existing methods and corresponding statistics by a new taxonomy idea.Categorizing 162 application papers into 13 domains and giving introduction.Some opening questions are discussed at the end of this manuscript. Rare events, especially those that could potentially negatively impact society, often require humans decision-making responses. Detecting rare events can be viewed as a prediction task in data mining and machine learning communities. As these events are rarely observed in daily life, the prediction task suffers from a lack of balanced data. In this paper, we provide an in depth review of rare event detection from an imbalanced learning perspective. Five hundred and seventeen related papers that have been published in the past decade were collected for the study. The initial statistics suggested that rare events detection and imbalanced learning are concerned across a wide range of research areas from management science to engineering. We reviewed all collected papers from both a technical and a practical point of view. Modeling methods discussed include techniques such as data preprocessing, classification algorithms and model evaluation. For applications, we first provide a comprehensive taxonomy of the existing application domains of imbalanced learning, and then we detail the applications for each category. Finally, some suggestions from the reviewed papers are incorporated with our experiences and judgments to offer further research directions for the imbalanced learning and rare event detection fields.

Learning from class-imbalanced data

Recently ensemble methods like ADABOOST have been applied successfully in many problems, while seemingly defying the problems of overfitting.

ADABOOST rarely overfits in the low noise regime, however, we show that it clearly does so for higher noise levels. Central to the understanding of this fact is the margin distribution. ADABOOST can be viewed as a constraint gradient descent in an error function with respect to the margin. We find that ADABOOST asymptotically achieves a hard margin distribution, i.e. the algorithm concentrates its resources on a few hard-to-learn patterns that are interestingly very similar to Support Vectors. A hard margin is clearly a sub-optimal strategy in the noisy case, and regularization, in our case a “mistrust” in the data, must be introduced in the algorithm to alleviate the distortions that single difficult patterns (e.g. outliers) can cause to the margin distribution. We propose several regularization methods and generalizations of the original ADABOOST algorithm to achieve a soft margin. In particular we suggest (1) regularized ADABOOSTREG where the gradient decent is done directly with respect to the soft margin and (2) regularized linear and quadratic programming (LP/QP-) ADABOOST, where the soft margin is attained by introducing slack variables.

Extensive simulations demonstrate that the proposed regularized ADABOOST-type algorithms are useful and yield competitive results for noisy data.

/pdf/soft-margins-for-adaboost-4d7guxy68r.pdf

Soft Margins for AdaBoost

In this paper we analyze several models of 1-way quantum finite automata, in the light of formal power series theory. In this general context, we recall two well known constructions, by proving: 1. Languages generated with isolated cut-point by a class of bounded rational formal series are regular. 2. If a class of formal series is closed under f-complement, Hadamard product and convex linear combination, then the class of languages generated with isolated cut-point is closed under boolean operations.

We introduce a general model of 1-way quantum automata and we compare their behaviors with those of measure-once, measure-many and reversible 1-way quantum automata.

Quantum computing: 1-way quantum automata

https://air.unimi.it/bitstream/2434/9370/4/rs-nc.pdf

Letters: Bio-molecular cancer prediction with random subspace ensembles of support vector machines

Implicit parallelism in genetic algorithms

A new boosting algorithm ADABOOST-Ra for regression problems is presented and upper bound on the error is obtained. Experimental results to compare ADABOOST-RΔ and other learning algorithms are given.

/pdf/a-boosting-algorithm-for-regression-3tvspzuj8s.pdf

A Boosting Algorithm for Regression

In this paper we analyze some features of the behaviour of quantum automata. In particular we prove that the class of languages recognized by quantum automata with isolated cut point is the class of reversible regular languages. As a more general result, we give a bound on the inverse error that implies the regularity of the language accepted by a quantum automaton.

Alberto Bertoni

Papers

Quantum computing: 1-way quantum automata

Letters: Bio-molecular cancer prediction with random subspace ensembles of support vector machines

Implicit parallelism in genetic algorithms

A Boosting Algorithm for Regression

Regular Languages Accepted by Quantum Automata