Noise-Tolerant Learning, the Parity Problem, and the Statistical Query Model

We describe a slightly sub-exponential time algorithm for learning parity functions in the presence of random classification noise. This results in a polynomial-time algorithm for the case of parity functions that depend on only the first O(log n log log n) bits of input. This is the first known instance of an efficient noise-tolerant algorithm for a concept class that is provably not learnable in the Statistical Query model of Kearns. Thus, we demonstrate that the set of problems learnable in the statistical query model is a strict subset of those problems learnable in the presence of noise in the PAC model. In coding-theory terms, what we give is a poly(n)-time algorithm for decoding linear k by n codes in the presence of random noise for the case of k = c log n loglog n for some c > 0. (The case of k = O(log n) is trivial since one can just individually check each of the 2^k possible messages and choose the one that yields the closest codeword.) A natural extension of the statistical query model is to allow queries about statistical properties that involve t-tuples of examples (as opposed to single examples). The second result of this paper is to show that any class of functions learnable (strongly or weakly) with t-wise queries for t = O(log n) is also weakly learnable with standard unary queries. Hence this natural extension to the statistical query model does not increase the set of weakly learnable functions

Statistical Active Learning Algorithms for Noise Tolerance and Differential Privacy

We describe a framework for designing efficient active learning algorithms that are tolerant to random classification noise and are differentially-private. The framework is based on active learning algorithms that are statistical in the sense that they rely on estimates of expectations of functions of filtered random examples. It builds on the powerful statistical query framework of Kearns (1993). We show that any efficient active statistical learning algorithm can be automatically converted to an efficient active learning algorithm which is tolerant to random classification noise as well as other forms of "uncorrelated" noise. The complexity of the resulting algorithms has information-theoretically optimal quadratic dependence on $1/(1-2\eta)$, where $\eta$ is the noise rate. We show that commonly studied concept classes including thresholds, rectangles, and linear separators can be efficiently actively learned in our framework. These results combined with our generic conversion lead to the first computationally-efficient algorithms for actively learning some of these concept classes in the presence of random classification noise that provide exponential improvement in the dependence on the error $\epsilon$ over their passive counterparts. In addition, we show that our algorithms can be automatically converted to efficient active differentially-private algorithms. This leads to the first differentially-private active learning algorithms with exponential label savings over the passive case.Comment: Extended abstract appears in NIPS 201

An Analysis of Active Learning With Uniform Feature Noise

In active learning, the user sequentially chooses values for feature $X$ and an oracle returns the corresponding label $Y$. In this paper, we consider the effect of feature noise in active learning, which could arise either because $X$ itself is being measured, or it is corrupted in transmission to the oracle, or the oracle returns the label of a noisy version of the query point. In statistics, feature noise is known as "errors in variables" and has been studied extensively in non-active settings. However, the effect of feature noise in active learning has not been studied before. We consider the well-known Berkson errors-in-variables model with additive uniform noise of width $\sigma$. Our simple but revealing setting is that of one-dimensional binary classification setting where the goal is to learn a threshold (point where the probability of a $+$ label crosses half). We deal with regression functions that are antisymmetric in a region of size $\sigma$ around the threshold and also satisfy Tsybakov's margin condition around the threshold. We prove minimax lower and upper bounds which demonstrate that when $\sigma$ is smaller than the minimiax active/passive noiseless error derived in \cite{CN07}, then noise has no effect on the rates and one achieves the same noiseless rates. For larger $\sigma$, the \textit{unflattening} of the regression function on convolution with uniform noise, along with its local antisymmetry around the threshold, together yield a behaviour where noise \textit{appears} to be beneficial. Our key result is that active learning can buy significant improvement over a passive strategy even in the presence of feature noise.Comment: 24 pages, 2 figures, published in the proceedings of the 17th International Conference on Artificial Intelligence and Statistics (AISTATS), 201

Robust Sound Event Classification using Deep Neural Networks

The automatic recognition of sound events by computers is an important aspect of emerging applications such as automated surveillance, machine hearing and auditory scene understanding. Recent advances in machine learning, as well as in computational models of the human auditory system, have contributed to advances in this increasingly popular research field. Robust sound event classification, the ability to recognise sounds under real-world noisy conditions, is an especially challenging task. Classification methods translated from the speech recognition domain, using features such as mel-frequency cepstral coefficients, have been shown to perform reasonably well for the sound event classification task, although spectrogram-based or auditory image analysis techniques reportedly achieve superior performance in noise. This paper outlines a sound event classification framework that compares auditory image front end features with spectrogram image-based front end features, using support vector machine and deep neural network classifiers. Performance is evaluated on a standard robust classification task in different levels of corrupting noise, and with several system enhancements, and shown to compare very well with current state-of-the-art classification techniques

Noise Tolerance under Risk Minimization

In this paper we explore noise tolerant learning of classifiers. We formulate the problem as follows. We assume that there is an ${\bf unobservable}$ training set which is noise-free. The actual training set given to the learning algorithm is obtained from this ideal data set by corrupting the class label of each example. The probability that the class label of an example is corrupted is a function of the feature vector of the example. This would account for most kinds of noisy data one encounters in practice. We say that a learning method is noise tolerant if the classifiers learnt with the ideal noise-free data and with noisy data, both have the same classification accuracy on the noise-free data. In this paper we analyze the noise tolerance properties of risk minimization (under different loss functions), which is a generic method for learning classifiers. We show that risk minimization under 0-1 loss function has impressive noise tolerance properties and that under squared error loss is tolerant only to uniform noise; risk minimization under other loss functions is not noise tolerant. We conclude the paper with some discussion on implications of these theoretical results

Making Risk Minimization Tolerant to Label Noise

In many applications, the training data, from which one needs to learn a classifier, is corrupted with label noise. Many standard algorithms such as SVM perform poorly in presence of label noise. In this paper we investigate the robustness of risk minimization to label noise. We prove a sufficient condition on a loss function for the risk minimization under that loss to be tolerant to uniform label noise. We show that the $0-1$ loss, sigmoid loss, ramp loss and probit loss satisfy this condition though none of the standard convex loss functions satisfy it. We also prove that, by choosing a sufficiently large value of a parameter in the loss function, the sigmoid loss, ramp loss and probit loss can be made tolerant to non-uniform label noise also if we can assume the classes to be separable under noise-free data distribution. Through extensive empirical studies, we show that risk minimization under the $0-1$ loss, the sigmoid loss and the ramp loss has much better robustness to label noise when compared to the SVM algorithm

Robust Adaptive Median Binary Pattern for noisy texture classification and retrieval

Texture is an important cue for different computer vision tasks and applications. Local Binary Pattern (LBP) is considered one of the best yet efficient texture descriptors. However, LBP has some notable limitations, mostly the sensitivity to noise. In this paper, we address these criteria by introducing a novel texture descriptor, Robust Adaptive Median Binary Pattern (RAMBP). RAMBP based on classification process of noisy pixels, adaptive analysis window, scale analysis and image regions median comparison. The proposed method handles images with high noisy textures, and increases the discriminative properties by capturing microstructure and macrostructure texture information. The proposed method has been evaluated on popular texture datasets for classification and retrieval tasks, and under different high noise conditions. Without any train or prior knowledge of noise type, RAMBP achieved the best classification compared to state-of-the-art techniques. It scored more than $90\%$ under $50\%$ impulse noise densities, more than $95\%$ under Gaussian noised textures with standard deviation $\sigma = 5$, and more than $99\%$ under Gaussian blurred textures with standard deviation $\sigma = 1.25$. The proposed method yielded competitive results and high performance as one of the best descriptors in noise-free texture classification. Furthermore, RAMBP showed also high performance for the problem of noisy texture retrieval providing high scores of recall and precision measures for textures with high levels of noise