This study formulates the IR target detection as a binary classification problem of each pixel. Each pixel is associated with a label which indicates whether it is a target or background pixel. The optimal label set for all the pixels of an image maximizes aposteriori distribution of label configuration given the pixel intensities. The posterior probability is factored into (or proportional to) a conditional likelihood of the intensity values and a prior probability of label configuration. Each of these two probabilities are computed assuming a Markov Random Field (MRF) on both pixel intensities and their labels. In particular, this study enforces neighborhood dependency on both intensity values, by a Simultaneous Auto Regressive (SAR) model, and on labels, by an Auto-Logistic model. The parameters of these MRF models are learned from labeled examples. During testing, an MRF inference technique, namely Iterated Conditional Mode (ICM), produces the optimal label for each pixel. The detection performance is further improved by incorporating temporal information through background subtraction. High performances on benchmark datasets demonstrate effectiveness of this method for IR target detection.
In this paper, we discuss the method of Bayesian regression and its efficacy for predicting price variation of Bitcoin, a recently popularized virtual, cryptographic currency. Bayesian regression refers to utilizing empirical data as proxy to perform Bayesian inference. We utilize Bayesian regression for the so-called "latent source model". The Bayesian regression for "latent source model" was introduced and discussed by Chen, Nikolov and Shah (2013) and Bresler, Chen and Shah (2014) for the purpose of binary classification. They established theoretical as well as empirical efficacy of the method for the setting of binary classification. In this paper, instead we utilize it for predicting real-valued quantity, the price of Bitcoin. Based on this price prediction method, we devise a simple strategy for trading Bitcoin. The strategy is able to nearly double the investment in less than 60 day period when run against real data trace.
Ambiguity or uncertainty is a pervasive element of many real world decision making processes. Variation in decisions is a norm in this situation when the same problem is posed to different subjects. Psychological and metaphysical research had proven that decision making by human is subjective. It is influenced by many factors such as experience, age, background, etc. Scene understanding is one of the computer vision problems that fall into this category. Conventional methods relax this problem by assuming scene images are mutually exclusive; and therefore, focus on developing different approaches to perform the binary classification tasks. In this paper, we show that scene images are non-mutually exclusive, and propose the Fuzzy Qualitative Rank Classifier (FQRC) to tackle the aforementioned problems. The proposed FQRC provides a ranking interpretation instead of binary decision. Evaluations in term of qualitative and quantitative using large numbers and challenging public scene datasets have shown the effectiveness of our proposed method in modeling the non-mutually exclusive scene images.
Estimating the parameters of probabilistic models of language such as maxent models and probabilistic neural models is computationally difficult since it involves evaluating partition functions by summing over an entire vocabulary, which may be millions of word types in size. Two closely related strategies---noise contrastive estimation (Mnih and Teh, 2012; Mnih and Kavukcuoglu, 2013; Vaswani et al., 2013) and negative sampling (Mikolov et al., 2012; Goldberg and Levy, 2014)---have emerged as popular solutions to this computational problem, but some confusion remains as to which is more appropriate and when. This document explicates their relationships to each other and to other estimation techniques. The analysis shows that, although they are superficially similar, NCE is a general parameter estimation technique that is asymptotically unbiased, while negative sampling is best understood as a family of binary classification models that are useful for learning word representations but not as a general-purpose estimator.
Binary classification is a common statistical learning problem in which a model is estimated on a set of covariates for some outcome indicating the membership of one of two classes. In the literature, there exists a distinction between hard and soft classification. In soft classification, the conditional class probability is modeled as a function of the covariates. In contrast, hard classification methods only target the optimal prediction boundary. While hard and soft classification methods have been studied extensively, not much work has been done to compare the actual tasks of hard and soft classification. In this paper we propose a spectrum of statistical learning problems which span the hard and soft classification tasks based on fitting multiple decision rules to the data. By doing so, we reveal a novel collection of learning tasks of increasing complexity. We study the problems using the framework of large-margin classifiers and a class of piecewise linear convex surrogates, for which we derive statistical properties and a corresponding sub-gradient descent algorithm. We conclude by applying our approach to simulation settings and a magnetic resonance imaging (MRI) dataset from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study.
In this paper, we consider the matrix completion problem when the observations are one-bit measurements of some underlying matrix M, and in particular the observed samples consist only of ones and no zeros. This problem is motivated by modern applications such as recommender systems and social networks where only "likes" or "friendships" are observed. The problem of learning from only positive and unlabeled examples, called PU (positive-unlabeled) learning, has been studied in the context of binary classification. We consider the PU matrix completion problem, where an underlying real-valued matrix M is first quantized to generate one-bit observations and then a subset of positive entries is revealed. Under the assumption that M has bounded nuclear norm, we provide recovery guarantees for two different observation models: 1) M parameterizes a distribution that generates a binary matrix, 2) M is thresholded to obtain a binary matrix. For the first case, we propose a "shifted matrix completion" method that recovers M using only a subset of indices corresponding to ones, while for the second case, we propose a "biased matrix completion" method that recovers the (thresholded) binary matrix. Both methods yield strong error bounds --- if M is n by n, the Frobenius error is bounded as O(1/((1-rho)n), where 1-rho denotes the fraction of ones observed. This implies a sample complexity of O(n\log n) ones to achieve a small error, when M is dense and n is large. We extend our methods and guarantees to the inductive matrix completion problem, where rows and columns of M have associated features. We provide efficient and scalable optimization procedures for both the methods and demonstrate the effectiveness of the proposed methods for link prediction (on real-world networks consisting of over 2 million nodes and 90 million links) and semi-supervised clustering tasks.
This paper presents a spike-based model which employs neurons with functionally distinct dendritic compartments for classifying high dimensional binary patterns. The synaptic inputs arriving on each dendritic subunit are nonlinearly processed before being linearly integrated at the soma, giving the neuron a capacity to perform a large number of input-output mappings. The model utilizes sparse synaptic connectivity; where each synapse takes a binary value. The optimal connection pattern of a neuron is learned by using a simple hardware-friendly, margin enhancing learning algorithm inspired by the mechanism of structural plasticity in biological neurons. The learning algorithm groups correlated synaptic inputs on the same dendritic branch. Since the learning results in modified connection patterns, it can be incorporated into current event-based neuromorphic systems with little overhead. This work also presents a branch-specific spike-based version of this structural plasticity rule. The proposed model is evaluated on benchmark binary classification problems and its performance is compared against that achieved using Support Vector Machine (SVM) and Extreme Learning Machine (ELM) techniques. Our proposed method attains comparable performance while utilizing 10 to 50% less computational resources than the other reported techniques.
We study the sample complexity of multiclass prediction in several learning settings. For the PAC setting our analysis reveals a surprising phenomenon: In sharp contrast to binary classification, we show that there exist multiclass hypothesis classes for which some Empirical Risk Minimizers (ERM learners) have lower sample complexity than others. Furthermore, there are classes that are learnable by some ERM learners, while other ERM learners will fail to learn them. We propose a principle for designing good ERM learners, and use this principle to prove tight bounds on the sample complexity of learning {\em symmetric} multiclass hypothesis classes---classes that are invariant under permutations of label names. We further provide a characterization of mistake and regret bounds for multiclass learning in the online setting and the bandit setting, using new generalizations of Littlestone's dimension.
A widely-used tool for binary classification is the Support Vector Machine (SVM), a supervised learning technique that finds the "maximum margin" linear separator between the two classes. While SVMs have been well studied in the batch (offline) setting, there is considerably less work on the streaming (online) setting, which requires only a single pass over the data using sub-linear space. Existing streaming algorithms are not yet competitive with the batch implementation. In this paper, we use the formulation of the SVM as a minimum enclosing ball (MEB) problem to provide a streaming SVM algorithm based off of the blurred ball cover originally proposed by Agarwal and Sharathkumar. Our implementation consistently outperforms existing streaming SVM approaches and provides higher accuracies than libSVM on several datasets, thus making it competitive with the standard SVM batch implementation.
In this paper, we theoretically justify an approach popular among participants of the Higgs Boson Machine Learning Challenge to optimize approximate median significance (AMS). The approach is based on the following two-stage procedure. First, a real-valued function is learned by minimizing a surrogate loss for binary classification, such as logistic loss, on the training sample. Then, a threshold is tuned on a separate validation sample, by direct optimization of AMS. We show that the regret of the resulting (thresholded) classifier measured with respect to the squared AMS, is upperbounded by the regret of the underlying real-valued function measured with respect to the logistic loss. Hence, we prove that minimizing logistic surrogate is a consistent method of optimizing AMS.
Finding a good classifier is a multiobjective optimization problem with different error rates and the costs to be minimized. The receiver operating characteristic is widely used in the machine learning community to analyze the performance of parametric classifiers or sets of Pareto optimal classifiers. In order to directly compare two sets of classifiers the area (or volume) under the convex hull can be used as a scalar indicator for the performance of a set of classifiers in receiver operating characteristic space. Recently, the convex hull based multiobjective genetic programming algorithm was proposed and successfully applied to maximize the convex hull area for binary classification problems. The contribution of this paper is to extend this algorithm for dealing with higher dimensional problem formulations. In particular, we discuss problems where parsimony (or classifier complexity) is stated as a third objective and multi-class classification with three different true classification rates to be maximized. The design of the algorithm proposed in this paper is inspired by indicator-based evolutionary algorithms, where first a performance indicator for a solution set is established and then a selection operator is designed that complies with the performance indicator. In this case, the performance indicator will be the volume under the convex hull. The algorithm is tested and analyzed in a proof of concept study on different benchmarks that are designed for measuring its capability to capture relevant parts of a convex hull. Further benchmark and application studies on email classification and feature selection round up the analysis and assess robustness and usefulness of the new algorithm in real world settings.
We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sampled from a common distribution. We propose a communication-efficient distributed algorithm to minimize the overall empirical loss, which is the average of the local empirical losses. The algorithm is based on an inexact damped Newton method, where the inexact Newton steps are computed by a distributed preconditioned conjugate gradient method. We analyze its iteration complexity and communication efficiency for minimizing self-concordant empirical loss functions, and discuss the results for distributed ridge regression, logistic regression and binary classification with a smoothed hinge loss. In a standard setting for supervised learning, the required number of communication rounds of the algorithm does not increase with the sample size, and only grows slowly with the number of machines.
Recent studies in the literature have paid much attention to the sparsity in linear classification tasks. One motivation of imposing sparsity assumption on the linear discriminant direction is to rule out the noninformative features, making hardly contribution to the classification problem. Most of those work were focused on the scenarios of binary classification. In the presence of multi-class data, preceding researches recommended individually pairwise sparse linear discriminant analysis(LDA). However, further sparsity should be explored. In this paper, an estimator of grouped LASSO type is proposed to take advantage of sparsity for multi-class data. It enjoys appealing non-asymptotic properties which allows insignificant correlations among features. This estimator exhibits superior capability on both simulated and real data.
The problem of inferring an inductive invariant for verifying program safety can be formulated in terms of binary classification. This is a standard problem in machine learning: given a sample of good and bad points, one is asked to find a classifier that generalizes from the sample and separates the two sets. Here, the good points are the reachable states of the program, and the bad points are those that reach a safety property violation. Thus, a learned classifier is a candidate invariant. In this paper, we propose a new algorithm that uses decision trees to learn candidate invariants in the form of arbitrary Boolean combinations of numerical inequalities. We have used our algorithm to verify C programs taken from the literature. The algorithm is able to infer safe invariants for a range of challenging benchmarks and compares favorably to other ML-based invariant inference techniques. In particular, it scales well to large sample sets.
In this paper we present a non-invasive ambient intelligence framework for the semi-automatic analysis of non-verbal communication applied to the restorative justice field. In particular, we propose the use of computer vision and social signal processing technologies in real scenarios of Victim-Offender Mediations, applying feature extraction techniques to multi-modal audio-RGB-depth data. We compute a set of behavioral indicators that define communicative cues from the fields of psychology and observational methodology. We test our methodology on data captured in real world Victim-Offender Mediation sessions in Catalonia in collaboration with the regional government. We define the ground truth based on expert opinions when annotating the observed social responses. Using different state-of-the-art binary classification approaches, our system achieves recognition accuracies of 86% when predicting satisfaction, and 79% when predicting both agreement and receptivity. Applying a regression strategy, we obtain a mean deviation for the predictions between 0.5 and 0.7 in the range [1-5] for the computed social signals.
Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification probability of error for the case when the training and test data are drawn from the same distribution and for the case where there exists some mismatch between training and test distributions. We confirm the theoretical results by designing feature selection algorithms using the criteria from these bounds and by evaluating the algorithms on a series of pathological speech classification tasks.
This paper provides a theoretical and computational justification of the long held claim that of the similarity of the probit and logit link functions often used in binary classification. Despite this widespread recognition of the strong similarities between these two link functions, very few (if any) researchers have dedicated time to carry out a formal study aimed at establishing and characterizing firmly all the aspects of the similarities and differences. This paper proposes a definition of both structural and predictive equivalence of link functions-based binary regression models, and explores the various ways in which they are either similar or dissimilar. From a predictive analytics perspective, it turns out that not only are probit and logit perfectly predictively concordant, but the other link functions like cauchit and complementary log log enjoy very high percentage of predictive equivalence. Throughout this paper, simulated and real life examples demonstrate all the equivalence results that we prove theoretically.
This paper deals with the binary classification task when the target class has the lower probability of occurrence. In such situation, it is not possible to build a powerful classifier by using standard methods such as logistic regression, classification tree, discriminant analysis, etc. To overcome this short-coming of these methods which yield classifiers with low sensibility, we tackled the classification problem here through an approach based on the association rules learning. This approach has the advantage of allowing the identification of the patterns that are well correlated with the target class. Association rules learning is a well known method in the area of data-mining. It is used when dealing with large database for unsupervised discovery of local patterns that expresses hidden relationships between input variables. In considering association rules from a supervised learning point of view, a relevant set of weak classifiers is obtained from which one derives a classifier that performs well.
The F-measure, which has originally been introduced in information retrieval, is nowadays routinely used as a performance metric for problems such as binary classification, multi-label classification, and structured output prediction. Optimizing this measure is a statistically and computationally challenging problem, since no closed-form solution exists. Adopting a decision-theoretic perspective, this article provides a formal and experimental analysis of different approaches for maximizing the F-measure. We start with a Bayes-risk analysis of related loss functions, such as Hamming loss and subset zero-one loss, showing that optimizing such losses as a surrogate of the F-measure leads to a high worst-case regret. Subsequently, we perform a similar type of analysis for F-measure maximizing algorithms, showing that such algorithms are approximate, while relying on additional assumptions regarding the statistical distribution of the binary response variables. Furthermore, we present a new algorithm which is not only computationally efficient but also Bayes-optimal, regardless of the underlying distribution. To this end, the algorithm requires only a quadratic (with respect to the number of binary responses) number of parameters of the joint distribution. We illustrate the practical performance of all analyzed methods by means of experiments with multi-label classification problems.