Neural networks are commonly used as models for classification for a wide variety of tasks. Typically, a learned affine transformation is placed at the end of such models, yielding a per-class value used for classification. This classifier can have a vast number of parameters, which grows linearly with the number of possible classes, thus requiring increasingly more resources. In this work we argue that this classifier can be fixed, up to a global scale constant, with little or no loss of accuracy for most tasks, allowing memory and computational benefits. Moreover, we show that by initializing the classifier with a Hadamard matrix we can speed up inference as well. We discuss the implications for current understanding of neural network models.
It has been argued that in supervised classification tasks, in practice it may be more sensible to perform model selection with respect to some more focused model selection score, like the supervised (conditional) marginal likelihood, than with respect to the standard marginal likelihood criterion. However, for most Bayesian network models, computing the supervised marginal likelihood score takes exponential time with respect to the amount of observed data. In this paper, we consider diagnostic Bayesian network classifiers where the significant model parameters represent conditional distributi…
The convergence of simultaneous and marginal predictive classifiers under partition exchangeability in supervised classification is obtained. The result shows the asymptotic convergence of these classifiers under infinite amount of training or test data, such that after observing umpteen amount of data, the differences between these classifiers would be negligible. This is an important result from the practical perspective as under the presence of sufficiently large amount of data, one can replace the simpler marginal classifier with computationally more expensive simultaneous one.
University of Chicago（芝加哥大学）；California Institute of Technology（加州理工学院）
In this paper we derive an explicit formula for calculating the marginal likelihood of a given factorization of a categorical dataset. Since the marginal likelihood is proportional to the posterior probability of the factorization, these likelihoods can be used to order all possible factorizations and select the "best" way to factor the overall distribution from which the dataset is drawn. The best factorization can then be used to construct a Bayes classifier which benefits from factoring out mutually independent sets of variables.
Consider the binary classification problem of predicting a target variable $Y$ from a discrete feature vector $X = (X_1,...,X_d)$. When the probability distribution $\mathbb{P}(X,Y)$ is known, the optimal classifier, leading to the minimum misclassification rate, is given by the Maximum A-posteriori Probability decision rule. However, estimating the complete joint distribution $\mathbb{P}(X,Y)$ is computationally and statistically impossible for large values of $d$. An alternative approach is to first estimate some low order marginals of $\mathbb{P}(X,Y)$ and then design the classifier based o…
This paper presents the Nataf-Beta Random Field Classifier, a discriminative approach that extends the applicability of the Beta conjugate prior to classification problems. The approach's key feature is to model the probability of a class conditional on attribute values as a random field whose marginals are Beta distributed, and where the parameters of marginals are themselves described by random fields. Although the classification accuracy of the approach proposed does not statistically outperform the best accuracies reported in the literature, it ranks among the top tier for the six benchmar…
Data heterogeneity is an inherent challenge that hinders the performance of federated learning (FL). Recent studies have identified the biased classifiers of local models as the key bottleneck. Previous attempts have used classifier calibration after FL training, but this approach falls short in improving the poor feature representations caused by training-time classifier biases. Resolving the classifier bias dilemma in FL requires a full understanding of the mechanisms behind the classifier. Recent advances in neural collapse have shown that the classifiers and feature prototypes under perfec…
Institute of Information Transmission Problems（信息传输问题研究所）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）
We consider a problem of risk estimation for large-margin multi-class classifiers. We propose a novel risk bound for the multi-class classification problem. The bound involves the marginal distribution of the classifier and the Rademacher complexity of the hypothesis class. We prove that our bound is tight in the number of classes. Finally, we compare our bound with the related ones and provide a simplified version of the bound for the multi-class classification with kernel based hypotheses.
Deep Copula Classifier: Theory, Consistency, and Empirical Evaluation
Department of Mathematics, University of Louisiana at Lafayette（路易斯安那大学拉福莱分校数学系）；Department of Statistics, Formerly of Presidency College, Kolkata, India（印度加尔各答 Presidency College 统计学系）
University of Edinburgh（爱丁堡大学）；University of Cambridge（剑桥大学）
We derive a new asymptotic expansion for the global excess risk of a local-$k$-nearest neighbour classifier, where the choice of $k$ may depend upon the test point. This expansion elucidates conditions under which the dominant contribution to the excess risk comes from the decision boundary of the optimal Bayes classifier, but we also show that if these conditions are not satisfied, then the dominant contribution may arise from the tails of the marginal distribution of the features. Moreover, we prove that, provided the $d$-dimensional marginal distribution of the features has a finite $ρ$th m…
School of Computational Science and Engineering（计算科学与工程学院）；College of Computing（计算学院）；Georgia Institute of Technology（佐治亚理工学院）；Yahoo! Labs（雅虎实验室）
Many popular linear classifiers, such as logistic regression, boosting, or SVM, are trained by optimizing a margin-based risk function. Traditionally, these risk functions are computed based on a labeled dataset. We develop a novel technique for estimating such risks using only unlabeled data and the marginal label distribution. We prove that the proposed risk estimator is consistent on high-dimensional datasets and demonstrate it on synthetic and real-world data. In particular, we show how the estimate is used for evaluating classifiers in transfer learning, and for training classifiers with …
Deep neural networks for image-based screening and computer-aided diagnosis have achieved expert-level performance on various medical imaging modalities, including chest radiographs. Recently, several works have indicated that these state-of-the-art classifiers can be biased with respect to sensitive patient attributes, such as race or gender, leading to growing concerns about demographic disparities and discrimination resulting from algorithmic and model-based decision-making in healthcare. Fair machine learning has focused on mitigating such biases against disadvantaged or marginalised group…
The marginal Bayesian predictive classifiers (mBpc) as opposed to the simultaneous Bayesian predictive classifiers (sBpc), handle each data separately and hence tacitly assumes the independence of the observations. However, due to saturation in learning of generative model parameters, the adverse effect of this false assumption on the accuracy of mBpc tends to wear out in face of increasing amount of training data; guaranteeing the convergence of these two classifiers under de Finetti type of exchangeability. This result however, is far from trivial for the sequences generated under Partition …
Imagine Lab（想象实验室）；Université Paris Est / École des Ponts（巴黎东大学 / 国立路桥学校）
The focus of our work is speeding up evaluation of deep neural networks in retrieval scenarios, where conventional architectures may spend too much time on negative examples. We propose to replace a monolithic network with our novel cascade of feature-sharing deep classifiers, called OnionNet, where subsequent stages may add both new layers as well as new feature channels to the previous ones. Importantly, intermediate feature maps are shared among classifiers, preventing them from the necessity of being recomputed. To accomplish this, the model is trained end-to-end in a principled way under …
Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）
Recent work on discriminative segmental models has shown that they can achieve competitive speech recognition performance, using features based on deep neural frame classifiers. However, segmental models can be more challenging to train than standard frame-based approaches. While some segmental models have been successfully trained end to end, there is a lack of understanding of their training under different settings and with different losses. We investigate a model class based on recent successful approaches, consisting of a linear model that combines segmental features based on an LSTM fram…
Galatasaray University（加拉塔萨雷大学）；University of Burgundy（勃艮第大学）
The selection of the best classification algorithm for a given dataset is a very widespread problem, occuring each time one has to choose a classifier to solve a real-world problem. It is also a complex task with many important methodological decisions to make. Among those, one of the most crucial is the choice of an appropriate measure in order to properly assess the classification performance and rank the algorithms. In this article, we focus on this specific task. We present the most popular measures and compare their behavior through discrimination plots. We then discuss their properties f…
Galatasaray University（加拉塔萨雷大学）；University of Burgundy（勃艮第大学）
The selection of the best classification algorithm for a given dataset is a very widespread problem. It is also a complex one, in the sense it requires to make several important methodological choices. Among them, in this work we focus on the measure used to assess the classification performance and rank the algorithms. We present the most popular measures and discuss their properties. Despite the numerous measures proposed over the years, many of them turn out to be equivalent in this specific case, to have interpretation problems, or to be unsuitable for our purpose. Consequently, classic ov…
Griffith University（格里菲斯大学）；Water Resources University（水利大学）；University of Alberta（阿尔伯塔大学）
In this study, we introduce a new approach to combine multi-classifiers in an ensemble system. Instead of using numeric membership values encountered in fixed combining rules, we construct interval membership values associated with each class prediction at the level of meta-data of observation by using concepts of information granules. In the proposed method, uncertainty (diversity) of findings produced by the base classifiers is quantified by interval-based information granules. The discriminative decision model is generated by considering both the bounds and the length of the obtained interv…
A number of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov random field. Belief propagation, an iterative message-passing algorithm, computes exactly such marginals when the underlying graph is a tree. But it has gained its popularity as an efficient way to approximate them in the more general case, even if it can exhibits multiple fixed points and is not guaranteed to converge. In this paper, we express a new sufficient condition for local stability of a belief propagation fixed point in terms of the graph struc…
Continuous time Bayesian network classifiers are designed for temporal classification of multivariate streaming data when time duration of events matters and the class does not change over time. This paper introduces the CTBNCToolkit: an open source Java toolkit which provides a stand-alone application for temporal classification and a library for continuous time Bayesian network classifiers. CTBNCToolkit implements the inference algorithm, the parameter learning algorithm, and the structural learning algorithm for continuous time Bayesian network classifiers. The structural learning algorithm…
Modern deep neural networks for classification usually jointly learn a backbone for representation and a linear classifier to output the logit of each class. A recent study has shown a phenomenon called neural collapse that the within-class means of features and the classifier vectors converge to the vertices of a simplex equiangular tight frame (ETF) at the terminal phase of training on a balanced dataset. Since the ETF geometric structure maximally separates the pair-wise angles of all classes in the classifier, it is natural to raise the question, why do we spend an effort to learn a classi…
Neural networks are widely used as a model for classification in a large variety of tasks. Typically, a learnable transformation (i.e. the classifier) is placed at the end of such models returning a value for each class used for classification. This transformation plays an important role in determining how the generated features change during the learning process. In this work, we argue that this transformation not only can be fixed (i.e. set as non-trainable) with no loss of accuracy and with a reduction in memory usage, but it can also be used to learn stationary and maximally separated embe…
Deep convolutional neural networks can be highly vulnerable to small perturbations of their inputs, potentially a major issue or limitation on system robustness when using deep networks as classifiers. In this paper we propose a low-cost method to explore marginal sample data near trained classifier decision boundaries, thus identifying potential adversarial samples. By finding such adversarial samples it is possible to reduce the search space of adversarial attack algorithms while keeping a reasonable successful perturbation rate. In our developed strategy, the potential adversarial samples r…
Google AI Perception（谷歌AI感知）；Department of Mathematics, UCLA（加州大学洛杉矶分校数学系）
In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_β$ score, area under the precision-recall curve, Precision at K, and more. The maximization of many of these metrics can be expressed as a constrained optimization problem, where the constraint is a function of the classifier's predictions. In this paper we propose a novel framework for learning with constraints that can be expressed as a predicted positive rate (or negative rate) on a subset of the training data. We e…
We propose a distributionally robust logistic regression model with an unfairness penalty that prevents discrimination with respect to sensitive attributes such as gender or ethnicity. This model is equivalent to a tractable convex optimization problem if a Wasserstein ball centered at the empirical distribution on the training data is used to model distributional uncertainty and if a new convex unfairness measure is used to incentivize equalized opportunities. We demonstrate that the resulting classifier improves fairness at a marginal loss of predictive accuracy on both synthetic and real da…
In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty estimates and a marginal likelihood objective, but their weak inductive biases lead to inferior accuracy. This has limited their applicability in certain tasks (e.g. image classification). We propose a translation-insensitive convolutional kernel, which relaxes the translation invariance constraint imposed by previous convolutional GPs. We show how we can use t…
Floating centroid method (FCM) offers an efficient way to solve a fixed-centroid problem for the neural network classifiers. However, evolutionary computation as its optimization method restrains the FCM to achieve satisfactory performance for different neural network structures, because of the high computational complexity and inefficiency. Traditional gradient-based methods have been extensively adopted to optimize the neural network classifiers. In this study, a gradient-based floating centroid (GDFC) method is introduced to address the fixed centroid problem for the neural network classifi…
Earlier studies have shown that classification accuracies of Bayesian networks (BNs) obtained by maximizing the conditional log likelihood (CLL) of a class variable, given the feature variables, were higher than those obtained by maximizing the marginal likelihood (ML). However, differences between the performances of the two scores in the earlier studies may be attributed to the fact that they used approximate learning algorithms, not exact ones. This paper compares the classification accuracies of BNs with approximate learning using CLL to those with exact learning using ML. The results demo…
We propose Very Simple Classifier (VSC) a novel method designed to incorporate the concepts of subsampling and locality in the definition of features to be used as the input of a perceptron. The rationale is that locality theoretically guarantees a bound on the generalization error. Each feature in VSC is a max-margin classifier built on randomly-selected pairs of samples. The locality in VSC is achieved by multiplying the value of the feature by a confidence measure that can be characterized in terms of the Chebichev inequality. The output of the layer is then fed in a output layer of neurons…
Pattern Recognition and Intelligent System Laboratory Beijing University of Posts and Telecommunications（北京邮电大学模式识别与智能系统实验室北京邮电大学）
In the design of brain-computer interface systems, classification of Electroencephalogram (EEG) signals is the essential part and a challenging task. Recently, as the marginalized discrete wavelet transform (mDWT) representations can reveal features related to the transient nature of the EEG signals, the mDWT coefficients have been frequently used in EEG signal classification. In our previous work, we have proposed a super-Dirichlet distribution-based classifier, which utilized the nonnegative and sum-to-one properties of the mDWT coefficients. The proposed classifier performed better than the…
This paper presents a batch classifier that has been improved from the earlier version and fixed a mistake in the earlier paper. Two important changes have been made. Each category is represented by a classifier, where each classifier classifies its own subset of data rows, using batch input values to represent the centroid. The first change is to use the category centroid as the desired category output. When the classifier represents more than one category, it creates a new layer and splits, to represent each category separately in the new layer. The second change therefore, is to allow the c…
In this paper, we investigate the usage of autoencoders in modeling textual data. Traditional autoencoders suffer from at least two aspects: scalability with the high dimensionality of vocabulary size and dealing with task-irrelevant words. We address this problem by introducing supervision via the loss function of autoencoders. In particular, we first train a linear classifier on the labeled data, then define a loss for the autoencoder with the weights learned from the linear classifier. To reduce the bias brought by one single classifier, we define a posterior probability distribution on the…
An approach to the acceleration of parametric weak classifier boosting is proposed. Weak classifier is called parametric if it has fixed number of parameters and, so, can be represented as a point into multidimensional space. Genetic algorithm is used instead of exhaustive search to learn parameters of such classifier. Proposed approach also takes cases when effective algorithm for learning some of the classifier parameters exists into account. Experiments confirm that such an approach can dramatically decrease classifier training time while keeping both training and test errors small.
