arXiv subjects

P. S. Sastry

Publications and source records attributed to P. S. Sastry.

At least 19 recordsLinked to original sources

arXiv2022

Adaptive Sample Selection for Robust Learning under Label Noise

Deep Neural Networks (DNNs) have been shown to be susceptible to memorization or overfitting in the presence of noisily-labelled data. For the problem of robust learning under such noisy data, several algorithms have been proposed. A prominent class of algorithms rely on sample selection strategies wherein, essentially, a fraction of samples with loss values below a certain threshold are selected for training. These algorithms are sensitive to such thresholds, and it is difficult to fix or learn these thresholds. Often, these algorithms also require information such as label noise rates which are typically unavailable in practice. In this paper, we propose an adaptive sample selection strategy that relies only on batch statistics of a given mini-batch to provide robustness against label noise. The algorithm does not have any additional hyperparameters for sample selection, does not need any information on noise rates and does not need access to separate data with clean labels. We empirically demonstrate the effectiveness of our algorithm on benchmark datasets.

cs.LG↗

arXiv2021

Memorization in Deep Neural Networks: Does the Loss Function matter?

Deep Neural Networks, often owing to the overparameterization, are shown to be capable of exactly memorizing even randomly labelled data. Empirical studies have also shown that none of the standard regularization techniques mitigate such overfitting. We investigate whether the choice of the loss function can affect this memorization. We empirically show, with benchmark data sets MNIST and CIFAR-10, that a symmetric loss function, as opposed to either cross-entropy or squared error loss, results in significant improvement in the ability of the network to resist such overfitting. We then provide a formal definition for robustness to memorization and provide a theoretical explanation as to why the symmetric losses provide this robustness. Our results clearly bring out the role loss functions alone can play in this phenomenon of memorization.

cs.LG↗

arXiv2019

Efficient Learning of Restricted Boltzmann Machines Using Covariance Estimates

Learning RBMs using standard algorithms such as CD(k) involves gradient descent on the negative log-likelihood. One of the terms in the gradient, which involves expectation w.r.t. the model distribution, is intractable and is obtained through an MCMC estimate. In this work we show that the Hessian of the log-likelihood can be written in terms of covariances of hidden and visible units and hence, all elements of the Hessian can also be estimated using the same MCMC samples with small extra computational costs. Since inverting the Hessian may be computationally expensive, we propose an algorithm that uses inverse of the diagonal approximation of the Hessian, instead. This essentially results in parameter-specific adaptive learning rates for the gradient descent process and improves the efficiency of learning RBMs compared to the standard methods. Specifically we show that using the inverse of diagonal approximation of Hessian in the stochastic DC (difference of convex functions) program approach results in very efficient learning of RBMs.

cs.LG↗

arXiv2019

PLUME: Polyhedral Learning Using Mixture of Experts

In this paper, we propose a novel mixture of expert architecture for learning polyhedral classifiers. We learn the parameters of the classifierusing an expectation maximization algorithm. Wederive the generalization bounds of the proposedapproach. Through an extensive simulation study, we show that the proposed method performs comparably to other state-of-the-art approaches.

cs.LG↗

arXiv2017

Robust Loss Functions under Label Noise for Deep Neural Networks

In many applications of classifier learning, training data suffers from label noise. Deep networks are learned using huge training data where the problem of noisy labels is particularly relevant. The current techniques proposed for learning deep networks under label noise focus on modifying the network architecture and on algorithms for estimating true labels from noisy labels. An alternate approach would be to look for loss functions that are inherently noise-tolerant. For binary classification there exist theoretical results on loss functions that are robust to label noise. In this paper, we provide some sufficient conditions on a loss function so that risk minimization under that loss function would be inherently tolerant to label noise for multiclass classification problems. These results generalize the existing results on noise-tolerant loss functions for binary classification. We study some of the widely used loss functions in deep networks and show that the loss function based on mean absolute value of error is inherently robust to label noise. Thus standard back propagation is enough to learn the true classifier even under label noise. Through experiments, we illustrate the robustness of risk minimization with such loss functions for learning neural networks.

stat.ML↗

arXiv2017

Learning RBM with a DC programming Approach

By exploiting the property that the RBM log-likelihood function is the difference of convex functions, we formulate a stochastic variant of the difference of convex functions (DC) programming to minimize the negative log-likelihood. Interestingly, the traditional contrastive divergence algorithm is a special case of the above formulation and the hyperparameters of the two algorithms can be chosen such that the amount of computation per mini-batch is identical. We show that for a given computational budget the proposed algorithm almost always reaches a higher log-likelihood more rapidly, compared to the standard contrastive divergence algorithm. Further, we modify this algorithm to use the centered gradients and show that it is more efficient and effective compared to the standard centered gradient algorithm on benchmark datasets.

cs.LG↗

arXiv2016

On the Robustness of Decision Tree Learning under Label Noise

In most practical problems of classifier learning, the training data suffers from the label noise. Hence, it is important to understand how robust is a learning algorithm to such label noise. This paper presents some theoretical analysis to show that many popular decision tree algorithms are robust to symmetric label noise under large sample size. We also present some sample complexity results which provide some bounds on the sample size for the robustness to hold with a high probability. Through extensive simulations we illustrate this robustness.

cs.LG↗

arXiv2015

Empirical Analysis of Sampling Based Estimators for Evaluating RBMs

The Restricted Boltzmann Machines (RBM) can be used either as classifiers or as generative models. The quality of the generative RBM is measured through the average log-likelihood on test data. Due to the high computational complexity of evaluating the partition function, exact calculation of test log-likelihood is very difficult. In recent years some estimation methods are suggested for approximate computation of test log-likelihood. In this paper we present an empirical comparison of the main estimation methods, namely, the AIS algorithm for estimating the partition function, the CSL method for directly estimating the log-likelihood, and the RAISE algorithm that combines these two ideas. We use the MNIST data set to learn the RBM and then compare these methods for estimating the test log-likelihood.

cs.LG↗

arXiv2015

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.

cs.LG↗

arXiv2014

Discovering Compressing Serial Episodes from Event Sequences

Most pattern mining methods output a very large number of frequent patterns and isolating a small but relevant subset is a challenging problem of current interest in frequent pattern mining. In this paper we consider discovery of a small set of relevant frequent episodes from data sequences. We make use of the Minimum Description Length principle to formulate the problem of selecting a subset of episodes. Using an interesting class of serial episodes with inter-event constraints and a novel encoding scheme for data using such episodes, we present algorithms for discovering small set of episodes that achieve good data compression. Using an example of the data streams obtained from distributed sensors in a composable coupled conveyor system, we show that our method is very effective in unearthing highly relevant episodes and that our scheme also achieves good data compression.

cs.DB↗

arXiv2014

Polyceptron: A Polyhedral Learning Algorithm

In this paper we propose a new algorithm for learning polyhedral classifiers which we call as Polyceptron. It is a Perception like algorithm which updates the parameters only when the current classifier misclassifies any training data. We give both batch and online version of Polyceptron algorithm. Finally we give experimental results to show the effectiveness of our approach.

cs.LG↗

arXiv2013

K-Plane Regression

In this paper, we present a novel algorithm for piecewise linear regression which can learn continuous as well as discontinuous piecewise linear functions. The main idea is to repeatedly partition the data and learn a liner model in in each partition. While a simple algorithm incorporating this idea does not work well, an interesting modification results in a good algorithm. The proposed algorithm is similar in spirit to $k$-means clustering algorithm. We show that our algorithm can also be viewed as an EM algorithm for maximum likelihood estimation of parameters under a reasonable probability model. We empirically demonstrate the effectiveness of our approach by comparing its performance with the state of art regression learning algorithms on some real world datasets.

cs.LG↗

arXiv2012

Geometric Decision Tree

In this paper we present a new algorithm for learning oblique decision trees. Most of the current decision tree algorithms rely on impurity measures to assess the goodness of hyperplanes at each node while learning a decision tree in a top-down fashion. These impurity measures do not properly capture the geometric structures in the data. Motivated by this, our algorithm uses a strategy to assess the hyperplanes in such a way that the geometric structure in the data is taken into account. At each node of the decision tree, we find the clustering hyperplanes for both the classes and use their angle bisectors as the split rule at that node. We show through empirical studies that this idea leads to small decision trees and better performance. We also present some analysis to show that the angle bisectors of clustering hyperplanes that we use as the split rules at each node, are solutions of an interesting optimization problem and hence argue that this is a principled method of learning a decision tree.

cs.LG↗

arXiv2012

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.

cs.LG↗

arXiv2010

A unified view of Automata-based algorithms for Frequent Episode Discovery

Frequent Episode Discovery framework is a popular framework in Temporal Data Mining with many applications. Over the years many different notions of frequencies of episodes have been proposed along with different algorithms for episode discovery. In this paper we present a unified view of all such frequency counting algorithms. We present a generic algorithm such that all current algorithms are special cases of it. This unified view allows one to gain insights into different frequencies and we present quantitative relationships among different frequencies. Our unified view also helps in obtaining correctness proofs for various algorithms as we show here. We also point out how this unified view helps us to consider generalization of the algorithm so that they can discover episodes with general partial orders.

cs.AI↗

arXiv2010

Efficient Discovery of Large Synchronous Events in Neural Spike Streams

We address the problem of finding patterns from multi-neuronal spike trains that give us insights into the multi-neuronal codes used in the brain and help us design better brain computer interfaces. We focus on the synchronous firings of groups of neurons as these have been shown to play a major role in coding and communication. With large electrode arrays, it is now possible to simultaneously record the spiking activity of hundreds of neurons over large periods of time. Recently, techniques have been developed to efficiently count the frequency of synchronous firing patterns. However, when the number of neurons being observed grows they suffer from the combinatorial explosion in the number of possible patterns and do not scale well. In this paper, we present a temporal data mining scheme that overcomes many of these problems. It generates a set of candidate patterns from frequent patterns of smaller size; all possible patterns are not counted. Also we count only a certain well defined subset of occurrences and this makes the process more efficient. We highlight the computational advantage that this approach offers over the existing methods through simulations. We also propose methods for assessing the statistical significance of the discovered patterns. We detect only those patterns that repeat often enough to be significant and thus be able to automatically fix the threshold for the data-mining application. Finally we discuss the usefulness of these methods for brain computer interfaces.

cs.NE↗

arXiv2009

Discovering general partial orders in event streams

Frequent episode discovery is a popular framework for pattern discovery in event streams. An episode is a partially ordered set of nodes with each node associated with an event type. Efficient (and separate) algorithms exist for episode discovery when the associated partial order is total (serial episode) and trivial (parallel episode). In this paper, we propose efficient algorithms for discovering frequent episodes with general partial orders. These algorithms can be easily specialized to discover serial or parallel episodes. Also, the algorithms are flexible enough to be specialized for mining in the space of certain interesting subclasses of partial orders. We point out that there is an inherent combinatorial explosion in frequent partial order mining and most importantly, frequency alone is not a sufficient measure of interestingness. We propose a new interestingness measure for general partial order episodes and a discovery method based on this measure, for filtering out uninteresting partial orders. Simulations demonstrate the effectiveness of our algorithms.

cs.AI↗

arXiv2009

Temporal data mining for root-cause analysis of machine faults in automotive assembly lines

Engine assembly is a complex and heavily automated distributed-control process, with large amounts of faults data logged everyday. We describe an application of temporal data mining for analyzing fault logs in an engine assembly plant. Frequent episode discovery framework is a model-free method that can be used to deduce (temporal) correlations among events from the logs in an efficient manner. In addition to being theoretically elegant and computationally efficient, frequent episodes are also easy to interpret in the form actionable recommendations. Incorporation of domain-specific information is critical to successful application of the method for analyzing fault logs in the manufacturing domain. We show how domain-specific knowledge can be incorporated using heuristic rules that act as pre-filters and post-filters to frequent episode discovery. The system described here is currently being used in one of the engine assembly plants of General Motors and is planned for adaptation in other plants. To the best of our knowledge, this paper presents the first real, large-scale application of temporal data mining in the manufacturing domain. We believe that the ideas presented in this paper can help practitioners engineer tools for analysis in other similar or related application domains as well.

cs.LG↗