arXiv subjects

Aditya Krishna Menon

Publications and source records attributed to Aditya Krishna Menon.

At least 55 records · Page 3Linked to original sources

arXiv2020

Noise-tolerant fair classification

Fairness-aware learning involves designing algorithms that do not discriminate with respect to some sensitive feature (e.g., race or gender). Existing work on the problem operates under the assumption that the sensitive feature available in one's training sample is perfectly reliable. This assumption may be violated in many real-world cases: for example, respondents to a survey may choose to conceal or obfuscate their group identity out of fear of potential discrimination. This poses the question of whether one can still learn fair classifiers given noisy sensitive features. In this paper, we answer the question in the affirmative: we show that if one measures fairness using the mean-difference score, and sensitive features are subject to noise from the mutually contaminated learning model, then owing to a simple identity we only need to change the desired fairness-tolerance. The requisite tolerance can be estimated by leveraging existing noise-rate estimators from the label noise literature. We finally show that our procedure is empirically effective on two case-studies involving sensitive feature censoring.

cs.LG↗

arXiv2020

Comparative Document Summarisation via Classification

This paper considers extractive summarisation in a comparative setting: given two or more document groups (e.g., separated by publication time), the goal is to select a small number of documents that are representative of each group, and also maximally distinguishable from other groups. We formulate a set of new objective functions for this problem that connect recent literature on document summarisation, interpretable machine learning, and data subset selection. In particular, by casting the problem as a binary classification amongst different groups, we derive objectives based on the notion of maximum mean discrepancy, as well as a simple yet effective gradient-based optimisation strategy. Our new formulation allows scalable evaluations of comparative summarisation as a classification task, both automatically and via crowd-sourcing. To this end, we evaluate comparative summarisation methods on a newly curated collection of controversial news topics over 13 months. We observe that gradient-based optimisation outperforms discrete and baseline approaches in 14 out of 24 different automatic evaluation settings. In crowd-sourced evaluations, summaries from gradient optimisation elicit 7% more accurate classification from human workers than discrete optimisation. Our result contrasts with recent literature on submodular data subset selection that favours discrete optimisation. We posit that our formulation of comparative summarisation will prove useful in a diverse range of use cases such as comparing content sources, authors, related topics, or distinct view points.

cs.IR↗

arXiv2019

Complementary-Label Learning for Arbitrary Losses and Models

In contrast to the standard classification paradigm where the true class is given to each training pattern, complementary-label learning only uses training patterns each equipped with a complementary label, which only specifies one of the classes that the pattern does not belong to. The goal of this paper is to derive a novel framework of complementary-label learning with an unbiased estimator of the classification risk, for arbitrary losses and models---all existing methods have failed to achieve this goal. Not only is this beneficial for the learning stage, it also makes model/hyper-parameter selection (through cross-validation) possible without the need of any ordinarily labeled validation data, while using any linear/non-linear models or convex/non-convex loss functions. We further improve the risk estimator by a non-negative correction and gradient ascent trick, and demonstrate its superiority through experiments.

stat.ML↗

arXiv2019

Online Hierarchical Clustering Approximations

Hierarchical clustering is a widely used approach for clustering datasets at multiple levels of granularity. Despite its popularity, existing algorithms such as hierarchical agglomerative clustering (HAC) are limited to the offline setting, and thus require the entire dataset to be available. This prohibits their use on large datasets commonly encountered in modern learning applications. In this paper, we consider hierarchical clustering in the online setting, where points arrive one at a time. We propose two algorithms that seek to optimize the Moseley and Wang (MW) revenue function, a variant of the Dasgupta cost. These algorithms offer different tradeoffs between efficiency and MW revenue performance. The first algorithm, OTD, is a highly efficient Online Top Down algorithm which provably achieves a 1/3-approximation to the MW revenue under a data separation assumption. The second algorithm, OHAC, is an online counterpart to offline HAC, which is known to yield a 1/3-approximation to the MW revenue, and produce good quality clusters in practice. We show that OHAC approximates offline HAC by leveraging a novel split-merge procedure. We empirically show that OTD and OHAC offer significant efficiency and cluster quality gains respectively over baselines.

cs.LG↗

arXiv2019

Monge blunts Bayes: Hardness Results for Adversarial Training

The last few years have seen a staggering number of empirical studies of the robustness of neural networks in a model of adversarial perturbations of their inputs. Most rely on an adversary which carries out local modifications within prescribed balls. None however has so far questioned the broader picture: how to frame a resource-bounded adversary so that it can be severely detrimental to learning, a non-trivial problem which entails at a minimum the choice of loss and classifiers. We suggest a formal answer for losses that satisfy the minimal statistical requirement of being proper. We pin down a simple sufficient property for any given class of adversaries to be detrimental to learning, involving a central measure of "harmfulness" which generalizes the well-known class of integral probability metrics. A key feature of our result is that it holds for all proper losses, and for a popular subset of these, the optimisation of this central measure appears to be independent of the loss. When classifiers are Lipschitz -- a now popular approach in adversarial training --, this optimisation resorts to optimal transport to make a low-budget compression of class marginals. Toy experiments reveal a finding recently separately observed: training against a sufficiently budgeted adversary of this kind improves generalization.

cs.LG↗

arXiv2019

On the Minimal Supervision for Training Any Binary Classifier from Only Unlabeled Data

Empirical risk minimization (ERM), with proper loss function and regularization, is the common practice of supervised classification. In this paper, we study training arbitrary (from linear to deep) binary classifier from only unlabeled (U) data by ERM. We prove that it is impossible to estimate the risk of an arbitrary binary classifier in an unbiased manner given a single set of U data, but it becomes possible given two sets of U data with different class priors. These two facts answer a fundamental question---what the minimal supervision is for training any binary classifier from only U data. Following these findings, we propose an ERM-based learning method from two sets of U data, and then prove it is consistent. Experiments demonstrate the proposed method could train deep models and outperform state-of-the-art methods for learning from two sets of U data.

stat.ML↗

arXiv2019

Fairness risk measures

Ensuring that classifiers are non-discriminatory or fair with respect to a sensitive feature (e.g., race or gender) is a topical problem. Progress in this task requires fixing a definition of fairness, and there have been several proposals in this regard over the past few years. Several of these, however, assume either binary sensitive features (thus precluding categorical or real-valued sensitive groups), or result in non-convex objectives (thus adversely affecting the optimisation landscape). In this paper, we propose a new definition of fairness that generalises some existing proposals, while allowing for generic sensitive features and resulting in a convex objective. The key idea is to enforce that the expected losses (or risks) across each subgroup induced by the sensitive feature are commensurate. We show how this relates to the rich literature on risk measures from mathematical finance. As a special case, this leads to a new convex fairness-aware objective based on minimising the conditional value at risk (CVaR).

cs.LG↗

arXiv2019

Cold-start Playlist Recommendation with Multitask Learning

Playlist recommendation involves producing a set of songs that a user might enjoy. We investigate this problem in three cold-start scenarios: (i) cold playlists, where we recommend songs to form new personalised playlists for an existing user; (ii) cold users, where we recommend songs to form new playlists for a new user; and (iii) cold songs, where we recommend newly released songs to extend users' existing playlists. We propose a flexible multitask learning method to deal with all three settings. The method learns from user-curated playlists, and encourages songs in a playlist to be ranked higher than those that are not by minimising a bipartite ranking loss. Inspired by an equivalence between bipartite ranking and binary classification, we show how one can efficiently approximate an optimal solution of the multitask learning objective by minimising a classification loss. Empirical results on two real playlist datasets show the proposed approach has good performance for cold-start playlist recommendation.

cs.IR↗

arXiv2019

Anomaly Detection using One-Class Neural Networks

We propose a one-class neural network (OC-NN) model to detect anomalies in complex data sets. OC-NN combines the ability of deep networks to extract a progressively rich representation of data with the one-class objective of creating a tight envelope around normal data. The OC-NN approach breaks new ground for the following crucial reason: data representation in the hidden layer is driven by the OC-NN objective and is thus customized for anomaly detection. This is a departure from other approaches which use a hybrid approach of learning deep features using an autoencoder and then feeding the features into a separate anomaly detection method like one-class SVM (OC-SVM). The hybrid OC-SVM approach is sub-optimal because it is unable to influence representational learning in the hidden layers. A comprehensive set of experiments demonstrate that on complex data sets (like CIFAR and GTSRB), OC-NN performs on par with state-of-the-art methods and outperformed conventional shallow methods in some scenarios.

cs.LG↗

arXiv2017

Revisiting revisits in trajectory recommendation

Trajectory recommendation is the problem of recommending a sequence of places in a city for a tourist to visit. It is strongly desirable for the recommended sequence to avoid loops, as tourists typically would not wish to revisit the same location. Given some learned model that scores sequences, how can we then find the highest-scoring sequence that is loop-free? This paper studies this problem, with three contributions. First, we detail three distinct approaches to the problem -- graph-based heuristics, integer linear programming, and list extensions of the Viterbi algorithm -- and qualitatively summarise their strengths and weaknesses. Second, we explicate how two ostensibly different approaches to the list Viterbi algorithm are in fact fundamentally identical. Third, we conduct experiments on real-world trajectory recommendation datasets to identify the tradeoffs imposed by each of the three approaches. Overall, our results indicate that a greedy graph-based heuristic offer excellent performance and runtime, leading us to recommend its use for removing loops at prediction time.

cs.LG↗

arXiv2017

Robust, Deep and Inductive Anomaly Detection

PCA is a classical statistical technique whose simplicity and maturity has seen it find widespread use as an anomaly detection technique. However, it is limited in this regard by being sensitive to gross perturbations of the input, and by seeking a linear subspace that captures normal behaviour. The first issue has been dealt with by robust PCA, a variant of PCA that explicitly allows for some data points to be arbitrarily corrupted, however, this does not resolve the second issue, and indeed introduces the new issue that one can no longer inductively find anomalies on a test set. This paper addresses both issues in a single model, the robust autoencoder. This method learns a nonlinear subspace that captures the majority of data points, while allowing for some data to have arbitrary corruption. The model is simple to train and leverages recent advances in the optimisation of deep neural networks. Experiments on a range of real-world datasets highlight the model's effectiveness.

cs.LG↗

arXiv2017

PathRec: Visual Analysis of Travel Route Recommendations

We present an interactive visualisation tool for recommending travel trajectories. This system is based on new machine learning formulations and algorithms for the sequence recommendation problem. The system starts from a map-based overview, taking an interactive query as starting point. It then breaks down contributions from different geographical and user behavior features, and those from individual points-of-interest versus pairs of consecutive points on a route. The system also supports detailed quantitative interrogation by comparing a large number of features for multiple points. Effective trajectory visualisations can potentially benefit a large cohort of online map users and assist their decision-making. More broadly, the design of this system can inform visualisations of other structured prediction tasks, such as for sequences or trees.

cs.HC↗

arXiv2017

f-GANs in an Information Geometric Nutshell

Nowozin \textit{et al} showed last year how to extend the GAN \textit{principle} to all $f$-divergences. The approach is elegant but falls short of a full description of the supervised game, and says little about the key player, the generator: for example, what does the generator actually converge to if solving the GAN game means convergence in some space of parameters? How does that provide hints on the generator's design and compare to the flourishing but almost exclusively experimental literature on the subject? In this paper, we unveil a broad class of distributions for which such convergence happens --- namely, deformed exponential families, a wide superset of exponential families --- and show tight connections with the three other key GAN parameters: loss, game and architecture. In particular, we show that current deep architectures are able to factorize a very large number of such densities using an especially compact design, hence displaying the power of deep architectures and their concinnity in the $f$-GAN game. This result holds given a sufficient condition on \textit{activation functions} --- which turns out to be satisfied by popular choices. The key to our results is a variational generalization of an old theorem that relates the KL divergence between regular exponential families and divergences between their natural parameters. We complete this picture with additional results and experimental insights on how these results may be used to ground further improvements of GAN architectures, via (i) a principled design of the activation functions in the generator and (ii) an explicit integration of proper composite losses' link function in the discriminator.

cs.LG↗

arXiv2017

Structured Recommendation

Current recommender systems largely focus on static, unstructured content. In many scenarios, we would like to recommend content that has structure, such as a trajectory of points-of-interests in a city, or a playlist of songs. Dubbed Structured Recommendation, this problem differs from the typical structured prediction problem in that there are multiple correct answers for a given input. Motivated by trajectory recommendation, we focus on sequential structures but in contrast to classical Viterbi decoding we require that valid predictions are sequences with no repeated elements. We propose an approach to sequence recommendation based on the structured support vector machine. For prediction, we modify the inference procedure to avoid predicting loops in the sequence. For training, we modify the objective function to account for the existence of multiple ground truths for a given input. We also modify the loss-augmented inference procedure to exclude the known ground truths. Experiments on real-world trajectory recommendation datasets show the benefits of our approach over existing, non-structured recommendation approaches.

cs.IR↗

arXiv2017

The cost of fairness in classification

We study the problem of learning classifiers with a fairness constraint, with three main contributions towards the goal of quantifying the problem's inherent tradeoffs. First, we relate two existing fairness measures to cost-sensitive risks. Second, we show that for cost-sensitive classification and fairness measures, the optimal classifier is an instance-dependent thresholding of the class-probability function. Third, we show how the tradeoff between accuracy and fairness is determined by the alignment between the class-probabilities for the target and sensitive features. Underpinning our analysis is a general framework that casts the problem of learning with a fairness requirement as one of minimising the difference of two statistical risks.

cs.LG↗

arXiv2016

A scaled Bregman theorem with applications

Bregman divergences play a central role in the design and analysis of a range of machine learning algorithms. This paper explores the use of Bregman divergences to establish reductions between such algorithms and their analyses. We present a new scaled isodistortion theorem involving Bregman divergences (scaled Bregman theorem for short) which shows that certain "Bregman distortions'" (employing a potentially non-convex generator) may be exactly re-written as a scaled Bregman divergence computed over transformed data. Admissible distortions include geodesic distances on curved manifolds and projections or gauge-normalisation, while admissible data include scalars, vectors and matrices. Our theorem allows one to leverage to the wealth and convenience of Bregman divergences when analysing algorithms relying on the aforementioned Bregman distortions. We illustrate this with three novel applications of our theorem: a reduction from multi-class density ratio to class-probability estimation, a new adaptive projection free yet norm-enforcing dual norm mirror descent algorithm, and a reduction from clustering on flat manifolds to clustering on curved manifolds. Experiments on each of these domains validate the analyses and suggest that the scaled Bregman theorem might be a worthy addition to the popular handful of Bregman divergence properties that have been pervasive in machine learning.

cs.LG↗

arXiv2016

Learning from Binary Labels with Instance-Dependent Corruption

Suppose we have a sample of instances paired with binary labels corrupted by arbitrary instance- and label-dependent noise. With sufficiently many such samples, can we optimally classify and rank instances with respect to the noise-free distribution? We provide a theoretical analysis of this question, with three main contributions. First, we prove that for instance-dependent noise, any algorithm that is consistent for classification on the noisy distribution is also consistent on the clean distribution. Second, we prove that for a broad class of instance- and label-dependent noise, a similar consistency result holds for the area under the ROC curve. Third, for the latter noise model, when the noise-free class-probability function belongs to the generalised linear model family, we show that the Isotron can efficiently and provably learn from the corrupted sample.

cs.LG↗

arXiv2015

Learning with Symmetric Label Noise: The Importance of Being Unhinged

Convex potential minimisation is the de facto approach to binary classification. However, Long and Servedio [2010] proved that under symmetric label noise (SLN), minimisation of any convex potential over a linear function class can result in classification performance equivalent to random guessing. This ostensibly shows that convex losses are not SLN-robust. In this paper, we propose a convex, classification-calibrated loss and prove that it is SLN-robust. The loss avoids the Long and Servedio [2010] result by virtue of being negatively unbounded. The loss is a modification of the hinge loss, where one does not clamp at zero; hence, we call it the unhinged loss. We show that the optimal unhinged solution is equivalent to that of a strongly regularised SVM, and is the limiting solution for any convex potential; this implies that strong l2 regularisation makes most standard learners SLN-robust. Experiments confirm the SLN-robustness of the unhinged loss.

cs.LG↗