This article describes an implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs. We consider a hierarchical Bayesian approach with a prior that is constructed by truncating a series expansion of the soft label function using the graph Laplacian eigenfunctions as basis functions. We compare our truncated prior to the untruncated Laplacian based prior in simulated and real data examples to illustrate the improved scalability in terms of size of the underlying graph.
Rotation-invariant face detection, i.e. detecting faces with arbitrary rotation-in-plane (RIP) angles, is widely required in unconstrained applications but still remains as a challenging task, due to the large variations of face appearances. Most existing methods compromise with speed or accuracy to handle the large RIP variations. To address this problem more efficiently, we propose Progressive Calibration Networks (PCN) to perform rotation-invariant face detection in a coarse-to-fine manner. PCN consists of three stages, each of which not only distinguishes the faces from non-faces, but also calibrates the RIP orientation of each face candidate to upright progressively. By dividing the calibration process into several progressive steps and only predicting coarse orientations in early stages, PCN can achieve precise and fast calibration. By performing binary classification of face vs. non-face with gradually decreasing RIP ranges, PCN can accurately detect faces with full $360^{\circ}$ RIP angles. Such designs lead to a real-time rotation-invariant face detector. The experiments on multi-oriented FDDB and a challenging subset of WIDER FACE containing rotated faces in the wild show that our PCN achieves quite promising performance.
In this paper we measured the stability of stochastic gradient method (SGM) for learning an approximated Fourier primal support vector machine. The stability of an algorithm is considered by measuring the generalization error in terms of the absolute difference between the test and the training error. Our problem is to learn an approximated kernel function using random Fourier features for a binary classification problem via online convex optimization settings. For a convex, Lipschitz continuous and smooth loss function, given reasonable number of iterations stochastic gradient method is stable. We showed that with a high probability SGM generalizes well for an approximated kernel under given assumptions.We empirically verified the theoretical findings for different parameters using several data sets.
In this paper, we examine the strength of deep learning technique for diagnosing lung cancer on medical image analysis problem. Convolutional neural networks (CNNs) models become popular among the pattern recognition and computer vision research area because of their promising outcome on generating high-level image representations. We propose a new deep learning architecture for learning high-level image representation to achieve high classification accuracy with low variance in medical image binary classification tasks. We aim to learn discriminant compact features at beginning of our deep convolutional neural network. We evaluate our model on Kaggle Data Science Bowl 2017 (KDSB17) data set, and compare it with some related works proposed in the Kaggle competition.
We report the findings of the second Complex Word Identification (CWI) shared task organized as part of the BEA workshop co-located with NAACL-HLT'2018. The second CWI shared task featured multilingual and multi-genre datasets divided into four tracks: English monolingual, German monolingual, Spanish monolingual, and a multilingual track with a French test set, and two tasks: binary classification and probabilistic classification. A total of 12 teams submitted their results in different task/track combinations and 11 of them wrote system description papers that are referred to in this report and appear in the BEA workshop proceedings.
We develop a new approach to solving classification problems, which is bases on the theory of coherent measures of risk and risk sharing ideas. The proposed approach aims at designing a risk-averse classifier. The new approach allows for associating distinct risk functional to each classes. The risk may be measured by different (non-linear in probability) measures, We analyze the structure of the new classifier design problem and establish its theoretical relation to known risk-neutral design problems. In particular, we show that the risk-sharing classification problem is equivalent to an implicitly defined optimization problem with unequal, implicitly defined but unknown, weights for each data point. We implement our methodology in a binary classification scenario on several different data sets and carry out numerical comparison with classifiers which are obtained using the Huber loss function and other loss functions known in the literature. We formulate specific risk-averse support vector machines in order to demonstrate the viability of our method.
We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this "learnability" even when given an amount of data that is too small to reliably learn any accurate model. Our first result applies to the setting where the data is drawn from a $d$-dimensional distribution with isotropic covariance (or known covariance), and the label of each datapoint is an arbitrary noisy function of the datapoint. In this setting, we show that with $O(\sqrt{d})$ samples, one can accurately estimate the fraction of the variance of the label that can be explained via the best linear function of the data. In contrast to this sublinear sample size, finding an approximation of the best-fit linear function requires on the order of $d$ samples. Our sublinear sample results and approach also extend to the non-isotropic setting, where the data distribution has an (unknown) arbitrary covariance matrix: we show that, if the label $y$ of point $x$ is a linear function with independent noise, $y = \langle x , \beta \rangle + noise$ with $\|\beta \|$ bounded, the variance of the noise can be estimated to error $\epsilon$ with $O(d^{1-1/\log{1/\epsilon}})$ if the covariance matrix has bounded condition number, or $O(d^{1-\sqrt{\epsilon}})$ if there are no bounds on the condition number. We also establish that these sample complexities are optimal, to constant factors. Finally, we extend these techniques to the setting of binary classification, where we obtain analogous sample complexities for the problem of estimating the prediction error of the best linear classifier, in a natural model of binary labeled data. We demonstrate the practical viability of our approaches on several real and synthetic datasets.
In the context of machine learning, disparate impact refers to a form of systematic discrimination whereby the output distribution of a model depends on the value of a sensitive attribute (e.g., race or gender). In this paper, we propose an information-theoretic framework to analyze the disparate impact of a binary classification model. We view the model as a fixed channel, and quantify disparate impact as the divergence in output distributions over two groups. Our aim is to find a correction function that can perturb the input distributions of each group to align their output distributions. We present an optimization problem that can be solved to obtain a correction function that will make the output distributions statistically indistinguishable. We derive closed-form expressions to efficiently compute the correction function, and demonstrate the benefits of our framework on a recidivism prediction problem based on the ProPublica COMPAS dataset.
In this paper, we have discussed a quantum approach for the all-pair multiclass classification problem. We have shown that the multiclass support vector machine for big data classification with a quantum all-pair approach can be implemented in logarithm runtime complexity on a quantum computer. In an all-pair approach, there is one binary classification problem for each pair of classes, and so there are k (k-1)/2 classifiers for a k-class problem. As compared to the classical multiclass support vector machine that can be implemented with polynomial run time complexity, our approach exhibits exponential speed up in the quantum version. The quantum all-pair algorithm can be used with other classification algorithms, and a speed up gain can be achieved as compared to their classical counterparts.
This article will devise data-driven, mathematical laws that generate optimal, statistical classification systems which achieve minimum error rates for data distributions with unchanging statistics. Thereby, I will design learning machines that minimize the expected risk or probability of misclassification. I will devise a system of fundamental equations of binary classification for a classification system in statistical equilibrium. I will use this system of equations to formulate the problem of learning unknown, linear and quadratic discriminant functions from data as a locus problem, thereby formulating geometric locus methods within a statistical framework. Solving locus problems involves finding equations of curves or surfaces defined by given properties and finding graphs or loci of given equations. I will devise three systems of data-driven, locus equations that generate optimal, statistical classification systems. Each class of learning machines satisfies fundamental statistical laws for a classification system in statistical equilibrium. Thereby, I will formulate three classes of learning machines that are scalable modules for optimal, statistical pattern recognition systems, all of which are capable of performing a wide variety of statistical pattern recognition tasks, where any given M-class statistical pattern recognition system exhibits optimal generalization performance for an M-class feature space.
The cost-sensitive classification problem plays a crucial role in mission-critical machine learning applications, and differs with traditional classification by taking the misclassification costs into consideration. Although being studied extensively in the literature, the fundamental limits of this problem are still not well understood. We investigate the hardness of this problem by extending the standard minimax lower bound of balanced binary classification problem (due to \cite{massart2006risk}), and emphasize the impact of cost terms on the hardness.
Adaptive optimization methods, which perform local optimization with a metric constructed from the history of iterates, are becoming increasingly popular for training deep neural networks. Examples include AdaGrad, RMSProp, and Adam. We show that for simple overparameterized problems, adaptive methods often find drastically different solutions than gradient descent (GD) or stochastic gradient descent (SGD). We construct an illustrative binary classification problem where the data is linearly separable, GD and SGD achieve zero test error, and AdaGrad, Adam, and RMSProp attain test errors arbitrarily close to half. We additionally study the empirical generalization capability of adaptive methods on several state-of-the-art deep learning models. We observe that the solutions found by adaptive methods generalize worse (often significantly worse) than SGD, even when these solutions have better training performance. These results suggest that practitioners should reconsider the use of adaptive methods to train neural networks.
One of the main difficulties in analyzing neural networks is the non-convexity of the loss function which may have many bad local minima. In this paper, we study the landscape of neural networks for binary classification tasks. Under mild assumptions, we prove that after adding one special neuron with a skip connection to the output, or one special neuron per layer, every local minimum is a global minimum.
In this paper, we present a kernel-based learning approach for the 2018 Complex Word Identification (CWI) Shared Task. Our approach is based on combining multiple low-level features, such as character n-grams, with high-level semantic features that are either automatically learned using word embeddings or extracted from a lexical knowledge base, namely WordNet. After feature extraction, we employ a kernel method for the learning phase. The feature matrix is first transformed into a normalized kernel matrix. For the binary classification task (simple versus complex), we employ Support Vector Machines. For the regression task, in which we have to predict the complexity level of a word (a word is more complex if it is labeled as complex by more annotators), we employ v-Support Vector Regression. We applied our approach only on the three English data sets containing documents from Wikipedia, WikiNews and News domains. Our best result during the competition was the third place on the English Wikipedia data set. However, in this paper, we also report better post-competition results.
Why are classifiers in high dimension vulnerable to "adversarial" perturbations? We show that it is likely not due to information theoretic limitations, but rather it could be due to computational constraints. First we prove that, for a broad set of classification tasks, the mere existence of a robust classifier implies that it can be found by a possibly exponential-time algorithm with relatively few training examples. Then we give a particular classification task where learning a robust classifier is computationally intractable. More precisely we construct a binary classification task in high dimensional space which is (i) information theoretically easy to learn robustly for large perturbations, (ii) efficiently learnable (non-robustly) by a simple linear separator, (iii) yet is not efficiently robustly learnable, even for small perturbations, by any algorithm in the statistical query (SQ) model. This example gives an exponential separation between classical learning and robust learning in the statistical query model. It suggests that adversarial examples may be an unavoidable byproduct of computational limitations of learning algorithms.
We apply the network Lasso to solve binary classification and clustering problems for network-structured data. To this end, we generalize ordinary logistic regression to non-Euclidean data with an intrinsic network structure. The resulting "logistic network Lasso" amounts to solving a non-smooth convex regularized empirical risk minimization. The risk is measured using the logistic loss incurred over a small set of labeled nodes. For the regularization, we propose to use the total variation of the classifier requiring it to conform to the underlying network structure. A scalable implementation of the learning method is obtained using an inexact variant of the alternating direction methods of multipliers which results in a scalable learning algorithm
Area under ROC (AUC) is an important metric for binary classification and bipartite ranking problems. However, it is difficult to directly optimizing AUC as a learning objective, so most existing algorithms are based on optimizing a surrogate loss to AUC. One significant drawback of these surrogate losses is that they require pairwise comparisons among training data, which leads to slow running time and increasing local storage for online learning. In this work, we describe a new surrogate loss based on a reformulation of the AUC risk, which does not require pairwise comparison but rankings of the predictions. We further show that the ranking operation can be avoided, and the learning objective obtained based on this surrogate enjoys linear complexity in time and storage. We perform experiments to demonstrate the effectiveness of the online and batch algorithms for AUC optimization based on the proposed surrogate loss.
Training accurate classifiers requires many labels, but each label provides only limited information (one bit for binary classification). In this work, we propose BabbleLabble, a framework for training classifiers in which an annotator provides a natural language explanation for each labeling decision. A semantic parser converts these explanations into programmatic labeling functions that generate noisy labels for an arbitrary amount of unlabeled data, which is used to train a classifier. On three relation extraction tasks, we find that users are able to train classifiers with comparable F1 scores from 5-100$\times$ faster by providing explanations instead of just labels. Furthermore, given the inherent imperfection of labeling functions, we find that a simple rule-based semantic parser suffices.
Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we introduce a random matrix-based framework to analyze the learning dynamics of a single-layer linear network on a binary classification problem, for data of simultaneously large dimension and size, trained by gradient descent. Our results provide rich insights into common questions in neural nets, such as overfitting, early stopping and the initialization of training, thereby opening the door for future studies of more elaborate structures and models appearing in today's neural networks.
Complex performance measures, beyond the popular measure of accuracy, are increasingly being used in the context of binary classification. These complex performance measures are typically not even decomposable, that is, the loss evaluated on a batch of samples cannot typically be expressed as a sum or average of losses evaluated at individual samples, which in turn requires new theoretical and methodological developments beyond standard treatments of supervised learning. In this paper, we advance this understanding of binary classification for complex performance measures by identifying two key properties: a so-called Karmic property, and a more technical threshold-quasi-concavity property, which we show is milder than existing structural assumptions imposed on performance measures. Under these properties, we show that the Bayes optimal classifier is a threshold function of the conditional probability of positive class. We then leverage this result to come up with a computationally practical plug-in classifier, via a novel threshold estimator, and further, provide a novel statistical analysis of classification error with respect to complex performance measures.