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Nisarg Shah

Publications and source records attributed to Nisarg Shah.

At least 37 records · Page 2Linked to original sources

How Far Can I Go ? : A Self-Supervised Approach for Deterministic Video Depth Forecasting

In this paper we present a novel self-supervised method to anticipate the depth estimate for a future, unobserved real-world urban scene. This work is the first to explore self-supervised learning for estimation of monocular depth of future unobserved frames of a video. Existing works rely on a large number of annotated samples to generate the probabilistic prediction of depth for unseen frames. However, this makes it unrealistic due to its requirement for large amount of annotated depth samples of video. In addition, the probabilistic nature of the case, where one past can have multiple future outcomes often leads to incorrect depth estimates. Unlike previous methods, we model the depth estimation of the unobserved frame as a view-synthesis problem, which treats the depth estimate of the unseen video frame as an auxiliary task while synthesizing back the views using learned pose. This approach is not only cost effective - we do not use any ground truth depth for training (hence practical) but also deterministic (a sequence of past frames map to an immediate future). To address this task we first develop a novel depth forecasting network DeFNet which estimates depth of unobserved future by forecasting latent features. Second, we develop a channel-attention based pose estimation network that estimates the pose of the unobserved frame. Using this learned pose, estimated depth map is reconstructed back into the image domain, thus forming a self-supervised solution. Our proposed approach shows significant improvements in Abs Rel metric compared to state-of-the-art alternatives on both short and mid-term forecasting setting, benchmarked on KITTI and Cityscapes. Code is available at https://github.com/sauradip/depthForecasting

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Class Fairness in Online Matching

In the classical version of online bipartite matching, there is a given set of offline vertices (aka agents) and another set of vertices (aka items) that arrive online. When each item arrives, its incident edges -- the agents who like the item -- are revealed and the algorithm must irrevocably match the item to such agents. We initiate the study of class fairness in this setting, where agents are partitioned into a set of classes and the matching is required to be fair with respect to the classes. We adopt popular fairness notions from the fair division literature such as envy-freeness (up to one item), proportionality, and maximin share fairness to our setting. Our class versions of these notions demand that all classes, regardless of their sizes, receive a fair treatment. We study deterministic and randomized algorithms for matching indivisible items (leading to integral matchings) and for matching divisible items (leading to fractional matchings). We design and analyze three novel algorithms. For matching indivisible items, we propose an adaptive-priority-based algorithm, MATCH-AND-SHIFT, prove that it achieves 1/2-approximation of both class envy-freeness up to one item and class maximin share fairness, and show that each guarantee is tight. For matching divisible items, we design a water-filling-based algorithm, EQUAL-FILLING, that achieves (1-1/e)-approximation of class envy-freeness and class proportionality; we prove (1-1/e) to be tight for class proportionality and establish a 3/4 upper bound on class envy-freeness. Finally, we build upon EQUAL-FILLING to design a randomized algorithm for matching indivisible items, EQAUL-FILLING-OCS, which achieves 0.593-approximation of class proportionality. The algorithm and its analysis crucially leverage the recently introduced technique of online correlated selection (OCS) [Fahrbach et al., 2020].

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How to Fairly Allocate Easy and Difficult Chores

A major open question in fair allocation of indivisible items is whether there always exists an allocation of chores that is Pareto optimal (PO) and envy-free up to one item (EF1). We answer this question affirmatively for the natural class of bivalued utilities, where each agent partitions the chores into easy and difficult ones, and has cost $p > 1$ for chores that are difficult for her and cost $1$ for chores that are easy for her. Such an allocation can be found in polynomial time using an algorithm based on the Fisher market. We also show that for a slightly broader class of utilities, where each agent $i$ can have a potentially different integer $p_i$, an allocation that is maximin share fair (MMS) always exists and can be computed in polynomial time, provided that each $p_i$ is an integer. Our MMS arguments also hold when allocating goods instead of chores, and extend to another natural class of utilities, namely weakly lexicographic utilities.

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The Metric Distortion of Multiwinner Voting

We extend the recently introduced framework of metric distortion to multiwinner voting. In this framework, $n$ agents and $m$ alternatives are located in an underlying metric space. The exact distances between agents and alternatives are unknown. Instead, each agent provides a ranking of the alternatives, ordered from the closest to the farthest. Typically, the goal is to select a single alternative that approximately minimizes the total distance from the agents, and the worst-case approximation ratio is termed distortion. In the case of multiwinner voting, the goal is to select a committee of $k$ alternatives that (approximately) minimizes the total cost to all agents. We consider the scenario where the cost of an agent for a committee is her distance from the $q$-th closest alternative in the committee. We reveal a surprising trichotomy on the distortion of multiwinner voting rules in terms of $k$ and $q$: The distortion is unbounded when $q \leq k/3$, asymptotically linear in the number of agents when $k/3 < q \leq k/2$, and constant when $q > k/2$.

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Two-Sided Matching Meets Fair Division

We introduce a new model for two-sided matching which allows us to borrow popular fairness notions from the fair division literature such as envy-freeness up to one good and maximin share guarantee. In our model, each agent is matched to multiple agents on the other side over whom she has additive preferences. We demand fairness for each side separately, giving rise to notions such as double envy-freeness up to one match (DEF1) and double maximin share guarantee (DMMS). We show that (a slight strengthening of) DEF1 cannot always be achieved, but in the special case where both sides have identical preferences, the round-robin algorithm with a carefully designed agent ordering achieves it. In contrast, DMMS cannot be achieved even when both sides have identical preferences.

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Fair and Efficient Resource Allocation with Partial Information

We study the fundamental problem of allocating indivisible goods to agents with additive preferences. We consider eliciting from each agent only a ranking of her $k$ most preferred goods instead of her full cardinal valuations. We characterize the value of $k$ needed to achieve envy-freeness up to one good and approximate maximin share guarantee, two widely studied fairness notions. We also analyze the multiplicative loss in social welfare incurred due to the lack of full information with and without the fairness requirements.

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Surprisingly Popular Voting Recovers Rankings, Surprisingly!

The wisdom of the crowd has long become the de facto approach for eliciting information from individuals or experts in order to predict the ground truth. However, classical democratic approaches for aggregating individual \emph{votes} only work when the opinion of the majority of the crowd is relatively accurate. A clever recent approach, \emph{surprisingly popular voting}, elicits additional information from the individuals, namely their \emph{prediction} of other individuals' votes, and provably recovers the ground truth even when experts are in minority. This approach works well when the goal is to pick the correct option from a small list, but when the goal is to recover a true ranking of the alternatives, a direct application of the approach requires eliciting too much information. We explore practical techniques for extending the surprisingly popular algorithm to ranked voting by partial votes and predictions and designing robust aggregation rules. We experimentally demonstrate that even a little prediction information helps surprisingly popular voting outperform classical approaches.

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Necessarily Optimal One-Sided Matchings

We study the classical problem of matching $n$ agents to $n$ objects, where the agents have ranked preferences over the objects. We focus on two popular desiderata from the matching literature: Pareto optimality and rank-maximality. Instead of asking the agents to report their complete preferences, our goal is to learn a desirable matching from partial preferences, specifically a matching that is necessarily Pareto optimal (NPO) or necessarily rank-maximal (NRM) under any completion of the partial preferences. We focus on the top-$k$ model in which agents reveal a prefix of their preference rankings. We design efficient algorithms to check if a given matching is NPO or NRM, and to check whether such a matching exists given top-$k$ partial preferences. We also study online algorithms for eliciting partial preferences adaptively, and prove bounds on their competitive ratio.

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Distortion in Social Choice Problems: The First 15 Years and Beyond

The notion of distortion in social choice problems has been defined to measure the loss in efficiency -- typically measured by the utilitarian social welfare, the sum of utilities of the participating agents -- due to having access only to limited information about the preferences of the agents. We survey the most significant results of the literature on distortion from the past 15 years, and highlight important open problems and the most promising avenues of ongoing and future work.

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Fair Algorithms for Multi-Agent Multi-Armed Bandits

We propose a multi-agent variant of the classical multi-armed bandit problem, in which there are $N$ agents and $K$ arms, and pulling an arm generates a (possibly different) stochastic reward for each agent. Unlike the classical multi-armed bandit problem, the goal is not to learn the "best arm"; indeed, each agent may perceive a different arm to be the best for her personally. Instead, we seek to learn a fair distribution over the arms. Drawing on a long line of research in economics and computer science, we use the Nash social welfare as our notion of fairness. We design multi-agent variants of three classic multi-armed bandit algorithms and show that they achieve sublinear regret, which is now measured in terms of the lost Nash social welfare.

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Optimal Bounds on the Price of Fairness for Indivisible Goods

In the allocation of resources to a set of agents, how do fairness guarantees impact the social welfare? A quantitative measure of this impact is the price of fairness, which measures the worst-case loss of social welfare due to fairness constraints. While initially studied for divisible goods, recent work on the price of fairness also studies the setting of indivisible goods. In this paper, we resolve the price of two well-studied fairness notions for the allocation of indivisible goods: envy-freeness up to one good (EF1), and approximate maximin share (MMS). For both EF1 and 1/2-MMS guarantees, we show, via different techniques, that the price of fairness is $O(\sqrt{n})$, where $n$ is the number of agents. From previous work, it follows that our bounds are tight. Our bounds are obtained via efficient algorithms. For 1/2-MMS, our bound holds for additive valuations, whereas for EF1, our bound holds for the more general class of subadditive valuations. This resolves an open problem posed by Bei et al. (2019).

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Fair Division with Binary Valuations: One Rule to Rule Them All

We study fair allocation of indivisible goods among agents. Prior research focuses on additive agent preferences, which leads to an impossibility when seeking truthfulness, fairness, and efficiency. We show that when agents have binary additive preferences, a compelling rule -- maximum Nash welfare (MNW) -- provides all three guarantees. Specifically, we show that deterministic MNW with lexicographic tie-breaking is group strategyproof in addition to being envy-free up to one good and Pareto optimal. We also prove that fractional MNW -- known to be group strategyproof, envy-free, and Pareto optimal -- can be implemented as a distribution over deterministic MNW allocations, which are envy-free up to one good. Our work establishes maximum Nash welfare as the ultimate allocation rule in the realm of binary additive preferences.

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Resolving the Optimal Metric Distortion Conjecture

We study the following metric distortion problem: there are two finite sets of points, $V$ and $C$, that lie in the same metric space, and our goal is to choose a point in $C$ whose total distance from the points in $V$ is as small as possible. However, rather than having access to the underlying distance metric, we only know, for each point in $V$, a ranking of its distances to the points in $C$. We propose algorithms that choose a point in $C$ using only these rankings as input and we provide bounds on their \emph{distortion} (worst-case approximation ratio). A prominent motivation for this problem comes from voting theory, where $V$ represents a set of voters, $C$ represents a set of candidates, and the rankings correspond to ordinal preferences of the voters. A major conjecture in this framework is that the optimal deterministic algorithm has distortion $3$. We resolve this conjecture by providing a polynomial-time algorithm that achieves distortion $3$, matching a known lower bound. We do so by proving a novel lemma about matching voters to candidates, which we refer to as the \emph{ranking-matching lemma}. This lemma induces a family of novel algorithms, which may be of independent interest, and we show that a special algorithm in this family achieves distortion $3$. We also provide more refined, parameterized, bounds using the notion of $α$-decisiveness, which quantifies the extent to which a voter may prefer her top choice relative to all others. Finally, we introduce a new randomized algorithm with improved distortion compared to known results, and also provide improved lower bounds on the distortion of all deterministic and randomized algorithms.

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The Effect of Strategic Noise in Linear Regression

We build on an emerging line of work which studies strategic manipulations in training data provided to machine learning algorithms. Specifically, we focus on the ubiquitous task of linear regression. Prior work focused on the design of strategyproof algorithms, which aim to prevent such manipulations altogether by aligning the incentives of data sources. However, algorithms used in practice are often not strategyproof, which induces a strategic game among the agents. We focus on a broad class of non-strategyproof algorithms for linear regression, namely $\ell_p$ norm minimization ($p > 1$) with convex regularization. We show that when manipulations are bounded, every algorithm in this class admits a unique pure Nash equilibrium outcome. We also shed light on the structure of this equilibrium by uncovering a surprising connection between strategyproof algorithms and pure Nash equilibria of non-strategyproof algorithms in a broader setting, which may be of independent interest. Finally, we analyze the quality of equilibria under these algorithms in terms of the price of anarchy.

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Best of Both Worlds: Ex-Ante and Ex-Post Fairness in Resource Allocation

We study the problem of allocating indivisible goods among agents with additive valuations. When randomization is allowed, it is possible to achieve compelling notions of fairness such as envy-freeness, which states that no agent should prefer any other agent's allocation to her own. When allocations must be deterministic, achieving exact fairness is impossible but approximate notions such as envy-freeness up to one good can be guaranteed. Our goal in this work is to achieve both simultaneously, by constructing a randomized allocation that is exactly fair ex-ante and approximately fair ex-post. The key question we address is whether ex-ante envy-freeness can be achieved in combination with ex-post envy-freeness up to one good. We settle this positively by designing an efficient algorithm that achieves both properties simultaneously. If we additionally require economic efficiency, we obtain an impossibility result. However, we show that economic efficiency and ex-ante envy-freeness can be simultaneously achieved if we slightly relax our ex-post fairness guarantee. On our way, we characterize the well-known Maximum Nash Welfare allocation rule in terms of a recently introduced fairness guarantee that applies to groups of agents, not just individuals.

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Participatory Budgeting: Models and Approaches

Participatory budgeting is a democratic approach to deciding the funding of public projects, which has been adopted in many cities across the world. We present a survey of research on participatory budgeting emerging from the computational social choice literature, which draws ideas from computer science and microeconomic theory. We present a mathematical model for participatory budgeting, which charts existing models across different axes including whether the projects are treated as "divisible" or "indivisible" and whether there are funding limits on individual projects. We then survey various approaches and methods from the literature, giving special emphasis on issues of preference elicitation, welfare objectives, fairness axioms, and voter incentives. Finally, we discuss several directions in which research on participatory budgeting can be extended in the future.

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Strategyproof Linear Regression in High Dimensions

This paper is part of an emerging line of work at the intersection of machine learning and mechanism design, which aims to avoid noise in training data by correctly aligning the incentives of data sources. Specifically, we focus on the ubiquitous problem of linear regression, where strategyproof mechanisms have previously been identified in two dimensions. In our setting, agents have single-peaked preferences and can manipulate only their response variables. Our main contribution is the discovery of a family of group strategyproof linear regression mechanisms in any number of dimensions, which we call generalized resistant hyperplane mechanisms. The game-theoretic properties of these mechanisms -- and, in fact, their very existence -- are established through a connection to a discrete version of the Ham Sandwich Theorem.

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Fair Allocation of Indivisible Public Goods

We consider the problem of fairly allocating indivisible public goods. We model the public goods as elements with feasibility constraints on what subsets of elements can be chosen, and assume that agents have additive utilities across elements. Our model generalizes existing frameworks such as fair public decision making and participatory budgeting. We study a groupwise fairness notion called the core, which generalizes well-studied notions of proportionality and Pareto efficiency, and requires that each subset of agents must receive an outcome that is fair relative to its size. In contrast to the case of divisible public goods (where fractional allocations are permitted), the core is not guaranteed to exist when allocating indivisible public goods. Our primary contributions are the notion of an additive approximation to the core (with a tiny multiplicative loss), and polynomial time algorithms that achieve a small additive approximation, where the additive factor is relative to the largest utility of an agent for an element. If the feasibility constraints define a matroid, we show an additive approximation of 2. A similar approach yields a constant additive bound when the feasibility constraints define a matching. More generally, if the feasibility constraints define an arbitrary packing polytope with mild restrictions, we show an additive guarantee that is logarithmic in the width of the polytope. Our algorithms are based on variants of the convex program for maximizing the Nash social welfare, but differ significantly from previous work in how it is used. Our guarantees are meaningful even when there are fewer elements than the number of agents. As far as we are aware, our work is the first to approximate the core in indivisible settings.

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