arXiv subjects

Anant Raj

Publications and source records attributed to Anant Raj.

At least 37 records · Page 2Linked to original sources

arXiv2022

MAViC: Multimodal Active Learning for Video Captioning

A large number of annotated video-caption pairs are required for training video captioning models, resulting in high annotation costs. Active learning can be instrumental in reducing these annotation requirements. However, active learning for video captioning is challenging because multiple semantically similar captions are valid for a video, resulting in high entropy outputs even for less-informative samples. Moreover, video captioning algorithms are multimodal in nature with a visual encoder and language decoder. Further, the sequential and combinatorial nature of the output makes the problem even more challenging. In this paper, we introduce MAViC which leverages our proposed Multimodal Semantics Aware Sequential Entropy (M-SASE) based acquisition function to address the challenges of active learning approaches for video captioning. Our approach integrates semantic similarity and uncertainty of both visual and language dimensions in the acquisition function. Our detailed experiments empirically demonstrate the efficacy of M-SASE for active learning for video captioning and improve on the baselines by a large margin.

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arXiv2022

Causal Feature Selection via Orthogonal Search

The problem of inferring the direct causal parents of a response variable among a large set of explanatory variables is of high practical importance in many disciplines. However, established approaches often scale at least exponentially with the number of explanatory variables, are difficult to extend to nonlinear relationships, and are difficult to extend to cyclic data. Inspired by {\em Debiased} machine learning methods, we study a one-vs.-the-rest feature selection approach to discover the direct causal parent of the response. We propose an algorithm that works for purely observational data while also offering theoretical guarantees, including the case of partially nonlinear relationships possibly under the presence of cycles. As it requires only one estimation for each variable, our approach is applicable even to large graphs. We demonstrate significant improvements compared to established approaches.

stat.ML↗

arXiv2021

Convergence of Uncertainty Sampling for Active Learning

Uncertainty sampling in active learning is heavily used in practice to reduce the annotation cost. However, there has been no wide consensus on the function to be used for uncertainty estimation in binary classification tasks and convergence guarantees of the corresponding active learning algorithms are not well understood. The situation is even more challenging for multi-category classification. In this work, we propose an efficient uncertainty estimator for binary classification which we also extend to multiple classes, and provide a non-asymptotic rate of convergence for our uncertainty sampling-based active learning algorithm in both cases under no-noise conditions (i.e., linearly separable data). We also extend our analysis to the noisy case and provide theoretical guarantees for our algorithm under the influence of noise in the task of binary and multi-class classification.

cs.LG↗

arXiv2020

Non-stationary Online Regression

Online forecasting under a changing environment has been a problem of increasing importance in many real-world applications. In this paper, we consider the meta-algorithm presented in \citet{zhang2017dynamic} combined with different subroutines. We show that an expected cumulative error of order $\tilde{O}(n^{1/3} C_n^{2/3})$ can be obtained for non-stationary online linear regression where the total variation of parameter sequence is bounded by $C_n$. Our paper extends the result of online forecasting of one-dimensional time-series as proposed in \cite{baby2019online} to general $d$-dimensional non-stationary linear regression. We improve the rate $O(\sqrt{n C_n})$ obtained by Zhang et al. 2017 and Besbes et al. 2015. We further extend our analysis to non-stationary online kernel regression. Similar to the non-stationary online regression case, we use the meta-procedure of Zhang et al. 2017 combined with Kernel-AWV (Jezequel et al. 2020) to achieve an expected cumulative controlled by the effective dimension of the RKHS and the total variation of the sequence. To the best of our knowledge, this work is the first extension of non-stationary online regression to non-stationary kernel regression. Lastly, we evaluate our method empirically with several existing benchmarks and also compare it with the theoretical bound obtained in this paper.

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arXiv2020

Dual Instrumental Variable Regression

We present a novel algorithm for non-linear instrumental variable (IV) regression, DualIV, which simplifies traditional two-stage methods via a dual formulation. Inspired by problems in stochastic programming, we show that two-stage procedures for non-linear IV regression can be reformulated as a convex-concave saddle-point problem. Our formulation enables us to circumvent the first-stage regression which is a potential bottleneck in real-world applications. We develop a simple kernel-based algorithm with an analytic solution based on this formulation. Empirical results show that we are competitive to existing, more complicated algorithms for non-linear instrumental variable regression.

stat.ML↗

arXiv2020

Stochastic Stein Discrepancies

Stein discrepancies (SDs) monitor convergence and non-convergence in approximate inference when exact integration and sampling are intractable. However, the computation of a Stein discrepancy can be prohibitive if the Stein operator - often a sum over likelihood terms or potentials - is expensive to evaluate. To address this deficiency, we show that stochastic Stein discrepancies (SSDs) based on subsampled approximations of the Stein operator inherit the convergence control properties of standard SDs with probability 1. Along the way, we establish the convergence of Stein variational gradient descent (SVGD) on unbounded domains, resolving an open question of Liu (2017). In our experiments with biased Markov chain Monte Carlo (MCMC) hyperparameter tuning, approximate MCMC sampler selection, and stochastic SVGD, SSDs deliver comparable inferences to standard SDs with orders of magnitude fewer likelihood evaluations.

stat.ML↗

arXiv2020

Model-specific Data Subsampling with Influence Functions

Model selection requires repeatedly evaluating models on a given dataset and measuring their relative performances. In modern applications of machine learning, the models being considered are increasingly more expensive to evaluate and the datasets of interest are increasing in size. As a result, the process of model selection is time-consuming and computationally inefficient. In this work, we develop a model-specific data subsampling strategy that improves over random sampling whenever training points have varying influence. Specifically, we leverage influence functions to guide our selection strategy, proving theoretically, and demonstrating empirically that our approach quickly selects high-quality models.

cs.LG↗

arXiv2020

Orthogonal Structure Search for Efficient Causal Discovery from Observational Data

The problem of inferring the direct causal parents of a response variable among a large set of explanatory variables is of high practical importance in many disciplines. Recent work exploits stability of regression coefficients or invariance properties of models across different experimental conditions for reconstructing the full causal graph. These approaches generally do not scale well with the number of the explanatory variables and are difficult to extend to nonlinear relationships. Contrary to existing work, we propose an approach which even works for observational data alone, while still offering theoretical guarantees including the case of partially nonlinear relationships. Our algorithm requires only one estimation for each variable and in our experiments we apply our causal discovery algorithm even to large graphs, demonstrating significant improvements compared to well established approaches.

stat.ML↗

arXiv2020

Explicit Regularization of Stochastic Gradient Methods through Duality

We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an explicit regularization framework as a minimum Bregman divergence convex feasibility problem. Using convex duality, we propose randomized Dykstra-style algorithms based on randomized dual coordinate ascent. For non-accelerated coordinate descent, we obtain an algorithm which bears strong similarities with (non-averaged) stochastic mirror descent on specific functions, as it is is equivalent for quadratic objectives, and equivalent in the early iterations for more general objectives. It comes with the benefit of an explicit convergence theorem to a minimum norm solution. For accelerated coordinate descent, we obtain a new algorithm that has better convergence properties than existing stochastic gradient methods in the interpolating regime. This leads to accelerated versions of the perceptron for generic $\ell_p$-norm regularizers, which we illustrate in experiments.

math.OC↗

arXiv2020

Importance Sampling via Local Sensitivity

Given a loss function $F:\mathcal{X} \rightarrow \R^+$ that can be written as the sum of losses over a large set of inputs $a_1,\ldots, a_n$, it is often desirable to approximate $F$ by subsampling the input points. Strong theoretical guarantees require taking into account the importance of each point, measured by how much its individual loss contributes to $F(x)$. Maximizing this importance over all $x \in \mathcal{X}$ yields the \emph{sensitivity score} of $a_i$. Sampling with probabilities proportional to these scores gives strong guarantees, allowing one to approximately minimize of $F$ using just the subsampled points. Unfortunately, sensitivity sampling is difficult to apply since (1) it is unclear how to efficiently compute the sensitivity scores and (2) the sample size required is often impractically large. To overcome both obstacles we introduce \emph{local sensitivity}, which measures data point importance in a ball around some center $x_0$. We show that the local sensitivity can be efficiently estimated using the \emph{leverage scores} of a quadratic approximation to $F$ and that the sample size required to approximate $F$ around $x_0$ can be bounded. We propose employing local sensitivity sampling in an iterative optimization method and analyze its convergence when $F$ is smooth and convex.

math.OC↗

arXiv2019

Sobolev Descent

We study a simplification of GAN training: the problem of transporting particles from a source to a target distribution. Starting from the Sobolev GAN critic, part of the gradient regularized GAN family, we show a strong relation with Optimal Transport (OT). Specifically with the less popular dynamic formulation of OT that finds a path of distributions from source to target minimizing a ``kinetic energy''. We introduce Sobolev descent that constructs similar paths by following gradient flows of a critic function in a kernel space or parametrized by a neural network. In the kernel version, we show convergence to the target distribution in the MMD sense. We show in theory and experiments that regularization has an important role in favoring smooth transitions between distributions, avoiding large gradients from the critic. This analysis in a simplified particle setting provides insight in paths to equilibrium in GANs.

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arXiv2019

On Matching Pursuit and Coordinate Descent

Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions. Exploiting the connection between the two algorithms, we present a unified analysis of both, providing affine invariant sublinear $\mathcal{O}(1/t)$ rates on smooth objectives and linear convergence on strongly convex objectives. As a byproduct of our affine invariant analysis of matching pursuit, our rates for steepest coordinate descent are the tightest known. Furthermore, we show the first accelerated convergence rate $\mathcal{O}(1/t^2)$ for matching pursuit and steepest coordinate descent on convex objectives.

stat.ML↗

arXiv2018

k-SVRG: Variance Reduction for Large Scale Optimization

Variance reduced stochastic gradient (SGD) methods converge significantly faster than the vanilla SGD counterpart. However, these methods are not very practical on large scale problems, as they either i) require frequent passes over the full data to recompute gradients---without making any progress during this time (like for SVRG), or ii)~they require additional memory that can surpass the size of the input problem (like for SAGA). In this work, we propose $k$-SVRG that addresses these issues by making best use of the \emph{available} memory and minimizes the stalling phases without progress. We prove linear convergence of $k$-SVRG on strongly convex problems and convergence to stationary points on non-convex problems. Numerical experiments show the effectiveness of our method.

math.OC↗

arXiv2018

A Differentially Private Kernel Two-Sample Test

Kernel two-sample testing is a useful statistical tool in determining whether data samples arise from different distributions without imposing any parametric assumptions on those distributions. However, raw data samples can expose sensitive information about individuals who participate in scientific studies, which makes the current tests vulnerable to privacy breaches. Hence, we design a new framework for kernel two-sample testing conforming to differential privacy constraints, in order to guarantee the privacy of subjects in the data. Unlike existing differentially private parametric tests that simply add noise to data, kernel-based testing imposes a challenge due to a complex dependence of test statistics on the raw data, as these statistics correspond to estimators of distances between representations of probability measures in Hilbert spaces. Our approach considers finite dimensional approximations to those representations. As a result, a simple chi-squared test is obtained, where a test statistic depends on a mean and covariance of empirical differences between the samples, which we perturb for a privacy guarantee. We investigate the utility of our framework in two realistic settings and conclude that our method requires only a relatively modest increase in sample size to achieve a similar level of power to the non-private tests in both settings.

stat.ML↗

arXiv2017

Sobolev GAN

We propose a new Integral Probability Metric (IPM) between distributions: the Sobolev IPM. The Sobolev IPM compares the mean discrepancy of two distributions for functions (critic) restricted to a Sobolev ball defined with respect to a dominant measure $μ$. We show that the Sobolev IPM compares two distributions in high dimensions based on weighted conditional Cumulative Distribution Functions (CDF) of each coordinate on a leave one out basis. The Dominant measure $μ$ plays a crucial role as it defines the support on which conditional CDFs are compared. Sobolev IPM can be seen as an extension of the one dimensional Von-Mises Cramér statistics to high dimensional distributions. We show how Sobolev IPM can be used to train Generative Adversarial Networks (GANs). We then exploit the intrinsic conditioning implied by Sobolev IPM in text generation. Finally we show that a variant of Sobolev GAN achieves competitive results in semi-supervised learning on CIFAR-10, thanks to the smoothness enforced on the critic by Sobolev GAN which relates to Laplacian regularization.

cs.LG↗

arXiv2017

Safe Adaptive Importance Sampling

Importance sampling has become an indispensable strategy to speed up optimization algorithms for large-scale applications. Improved adaptive variants - using importance values defined by the complete gradient information which changes during optimization - enjoy favorable theoretical properties, but are typically computationally infeasible. In this paper we propose an efficient approximation of gradient-based sampling, which is based on safe bounds on the gradient. The proposed sampling distribution is (i) provably the best sampling with respect to the given bounds, (ii) always better than uniform sampling and fixed importance sampling and (iii) can efficiently be computed - in many applications at negligible extra cost. The proposed sampling scheme is generic and can easily be integrated into existing algorithms. In particular, we show that coordinate-descent (CD) and stochastic gradient descent (SGD) can enjoy significant a speed-up under the novel scheme. The proven efficiency of the proposed sampling is verified by extensive numerical testing.

cs.LG↗

arXiv2017

Approximate Steepest Coordinate Descent

We propose a new selection rule for the coordinate selection in coordinate descent methods for huge-scale optimization. The efficiency of this novel scheme is provably better than the efficiency of uniformly random selection, and can reach the efficiency of steepest coordinate descent (SCD), enabling an acceleration of a factor of up to $n$, the number of coordinates. In many practical applications, our scheme can be implemented at no extra cost and computational efficiency very close to the faster uniform selection. Numerical experiments with Lasso and Ridge regression show promising improvements, in line with our theoretical guarantees.

cs.LG↗

arXiv2017

Local Group Invariant Representations via Orbit Embeddings

Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant representations. Locality is achieved by defining a suitable probability distribution over the group which in turn induces distributions in the input feature space. We learn a decision function over these distributions by appealing to the powerful framework of kernel methods and generate local invariant random feature maps via kernel approximations. We show uniform convergence bounds for kernel approximation and provide excess risk bounds for learning with these features. We evaluate our method on three real datasets, including Rotated MNIST and CIFAR-10, and observe that it outperforms competing kernel based approaches. The proposed method also outperforms deep CNN on Rotated-MNIST and performs comparably to the recently proposed group-equivariant CNN.

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