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Philips George John

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5 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Distribution Learning Meets Graph Structure Sampling

Arnab Bhattacharyya
Sutanu Gayen
Philips George John
Sayantan Sen
N. V. Vinodchandran

This work establishes a novel link between the problem of PAC-learning high-dimensional graphical models and the task of (efficient) counting and sampling of graph structures, using an online learning framework. The problem of efficiently counting and sampling graphical structures, such as spanning trees and acyclic orientations, has been a vibrant area of research in algorithms. We show that this rich algorithmic foundation can be leveraged to develop new algorithms for learning high-dimensional graphical models. We present the first efficient algorithm for (both realizable and agnostic) learning of Bayes nets with a chordal skeleton. In particular, we present an algorithm that, given integers $k, d > 0$, error parameter $\varepsilon > 0$, an undirected chordal graph $G$ on $n$ vertices, and sample access to a distribution $P^\ast$ on $[k]^n$; (1) returns a Bayes net $\widehat{P}$ with skeleton $G$ and indegree $d$, whose KL-divergence from $P^\ast$ is at most $\varepsilon$ more than the optimal KL-divergence between $P^\ast$ and any Bayes net with skeleton $G$ and indegree $d$, (2) uses $\widetilde{O}(n^3k^{d+1}/\varepsilon^2)$ samples from $P^\ast$ and runs in time $\mathrm{poly}(n, k, \varepsilon^{-1})$ for constant $d$. Prior results in this spirit were for only for trees ($d=1$, tree skeleton) via Chow-Liu, and in the realizable setting for polytrees (arbitrary $d$ but tree skeleton). Thus, our result significantly extends the state-of-the-art in learning Bayes net distributions. We also establish new results for learning tree and polytree distributions.

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ICML Conference 2025 Conference Paper

Learning multivariate Gaussians with imperfect advice

Arnab Bhattacharyya 0001
Davin Choo
Philips George John
Themis Gouleakis

We revisit the problem of distribution learning within the framework of learning-augmented algorithms. In this setting, we explore the scenario where a probability distribution is provided as potentially inaccurate advice on the true, unknown distribution. Our objective is to develop learning algorithms whose sample complexity decreases as the quality of the advice improves, thereby surpassing standard learning lower bounds when the advice is sufficiently accurate. Specifically, we demonstrate that this outcome is achievable for the problem of learning a multivariate Gaussian distribution $N(\mu, \Sigma)$ in the PAC learning setting. Classically, in the advice-free setting, $\widetilde{\Theta}(d^2/\varepsilon^2)$ samples are sufficient and worst case necessary to learn $d$-dimensional Gaussians up to TV distance $\varepsilon$ with constant probability. When we are additionally given a parameter $\widetilde{\Sigma}$ as advice, we show that $\widetilde{\mathcal{O}}(d^{2-\beta}/\varepsilon^2)$ samples suffices whenever $|| \widetilde{\Sigma}^{-1/2} \Sigma \widetilde{\Sigma}^{-1/2} - I_d ||_1 \leq \varepsilon d^{1-\beta}$ (where $||\cdot||_1$ denotes the entrywise $\ell_1$ norm) for any $\beta > 0$, yielding a polynomial improvement over the advice-free setting.

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AAAI Conference 2025 Conference Paper

p-Mean Regret for Stochastic Bandits

Anand Krishna
Philips George John
Adarsh Barik
Vincent Y. F. Tan

In this work, we extend the concept of the p-mean welfare objective from social choice theory to study p-mean regret in stochastic multi-armed bandit problems. The p-mean regret, defined as the difference between the optimal mean among the arms and the p-mean of the expected rewards, offers a flexible framework for evaluating bandit algorithms, enabling algorithm designers to balance fairness and efficiency by adjusting the parameter p. Our framework encompasses both average cumulative regret and Nash regret as special cases. We introduce a simple, unified UCB-based algorithm (Explore-Then-UCB) that achieves novel p-mean regret bounds. Our algorithm consists of two phases: a carefully calibrated uniform exploration phase to initialize sample means, followed by the UCB1 algorithm of Auer et al. (2002). Under mild assumptions, we prove that our algorithm achieves a p-mean regret bound of Otilde( sqrt( k / T^{1/(2|p|)} ) ) for all p <= -1, where k represents the number of arms and T the time horizon. When -1< p < 0, we achieve a regret bound of Otilde( sqrt( k^{1.5} / T^{1/2} ) ). For the range 0 < p <= 1, we achieve a p-mean regret scaling as Otilde( sqrt( k / T ) ), which matches the previously established lower bound up to logarithmic factors. This result stems from the fact that the p-mean regret of any algorithm is at least its average cumulative regret for p <= 1. In the case of Nash regret (the limit as p approaches zero), our unified approach differs from prior work of Barman et al. (2023), which requires a new Nash Confidence Bound algorithm. Notably, we achieve the same regret bound up to constant factors using our more general method.

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NeurIPS Conference 2025 Conference Paper

Product Distribution Learning with Imperfect Advice

Arnab Bhattacharyya
Choo, XianJun, Davin
Philips George John
Themis Gouleakis

Given i. i. d. ~samples from an unknown distribution $P$, the goal of distribution learning is to recover the parameters of a distribution that is close to $P$. When $P$ belongs to the class of product distributions on the Boolean hypercube $\{0, 1\}^d$, it is known that $\Omega(d/\epsilon^2)$ samples are necessary to learn $P$ within total variation (TV) distance $\epsilon$. We revisit this problem when the learner is also given as advice the parameters of a product distribution $Q$. We show that there is an efficient algorithm to learn $P$ within TV distance $\epsilon$ that has sample complexity $\tilde{O}(d^{1-\eta}/\epsilon^2)$, if $\|\mathbf{p} - \mathbf{q}\|_1<\epsilon d^{0. 5 - \Omega(\eta)}$. Here, $\mathbf{p}$ and $\mathbf{q}$ are the mean vectors of $P$ and $Q$ respectively, and no bound on $\|\mathbf{p} - \mathbf{q}\|_1$ is known to the algorithm a priori.

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UAI Conference 2020 Conference Paper

Verifying Individual Fairness in Machine Learning Models

Philips George John
Deepak Vijaykeerthy
Diptikalyan Saha

We consider the problem of whether a given decision model, working with structured data, has individual fairness. Following the work of Dwork, a model is individually biased (or unfair) if there is a pair of valid inputs which are close to each other (according to an appropriate metric) but are treated differently by the model (different class label, or large difference in output), and it is unbiased (or fair) if no such pair exists. Our objective is to construct verifiers for proving individual fairness of a given model, and we do so by considering appropriate relaxations of the problem. We construct verifiers which are sound but not complete for linear classifiers, and kernelized polynomial/radial basis function classifiers. We also report the experimental results of evaluating our proposed algorithms on publicly available datasets.

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