arXiv subjects

Anay Mehrotra

Publications and source records attributed to Anay Mehrotra.

At least 37 records · Page 2Linked to original sources

arXiv2025

What Makes Treatment Effects Identifiable? Characterizations and Estimators Beyond Unconfoundedness

Most of the widely used estimators of the average treatment effect (ATE) in causal inference rely on the assumptions of unconfoundedness and overlap. Unconfoundedness requires that the observed covariates account for all correlations between the outcome and treatment. Overlap requires the existence of randomness in treatment decisions for all individuals. Nevertheless, many types of studies frequently violate unconfoundedness or overlap, for instance, observational studies with deterministic treatment decisions - popularly known as Regression Discontinuity designs - violate overlap. In this paper, we initiate the study of general conditions that enable the identification of the average treatment effect, extending beyond unconfoundedness and overlap. In particular, following the paradigm of statistical learning theory, we provide an interpretable condition that is sufficient and necessary for the identification of ATE. Moreover, this condition also characterizes the identification of the average treatment effect on the treated (ATT) and can be used to characterize other treatment effects as well. To illustrate the utility of our condition, we present several well-studied scenarios where our condition is satisfied and, hence, we prove that ATE can be identified in regimes that prior works could not capture. For example, under mild assumptions on the data distributions, this holds for the models proposed by Tan (2006) and Rosenbaum (2002), and the Regression Discontinuity design model introduced by Thistlethwaite and Campbell (1960). For each of these scenarios, we also show that, under natural additional assumptions, ATE can be estimated from finite samples. We believe these findings open new avenues for bridging learning-theoretic insights and causal inference methodologies, particularly in observational studies with complex treatment mechanisms.

math.ST↗

arXiv2025

On Union-Closedness of Language Generation

We investigate language generation in the limit - a model by Kleinberg and Mullainathan [NeurIPS 2024] and extended by Li, Raman, and Tewari [COLT 2025]. While Kleinberg and Mullainathan proved generation is possible for all countable collections, Li et al. defined a hierarchy of generation notions (uniform, non-uniform, and generatable) and explored their feasibility for uncountable collections. Our first set of results resolve two open questions of Li et al. by proving finite unions of generatable or non-uniformly generatable classes need not be generatable. These follow from a stronger result: there is a non-uniformly generatable class and a uniformly generatable class whose union is non-generatable. This adds to the aspects along which language generation in the limit is different from traditional tasks in statistical learning theory like classification, which are closed under finite unions. In particular, it implies that given two generators for different collections, one cannot combine them to obtain a single "more powerful" generator, prohibiting this notion of boosting. Our construction also addresses a third open question of Li et al. on whether there are uncountable classes that are non-uniformly generatable and do not satisfy the eventually unbounded closure (EUC) condition introduced by Li, Raman, and Tewari. Our approach utilizes carefully constructed classes along with a novel diagonalization argument that could be of independent interest in the growing area of language generation.

cs.LG↗

arXiv2024

Tree of Attacks: Jailbreaking Black-Box LLMs Automatically

While Large Language Models (LLMs) display versatile functionality, they continue to generate harmful, biased, and toxic content, as demonstrated by the prevalence of human-designed jailbreaks. In this work, we present Tree of Attacks with Pruning (TAP), an automated method for generating jailbreaks that only requires black-box access to the target LLM. TAP utilizes an attacker LLM to iteratively refine candidate (attack) prompts until one of the refined prompts jailbreaks the target. In addition, before sending prompts to the target, TAP assesses them and prunes the ones unlikely to result in jailbreaks, reducing the number of queries sent to the target LLM. In empirical evaluations, we observe that TAP generates prompts that jailbreak state-of-the-art LLMs (including GPT4-Turbo and GPT4o) for more than 80% of the prompts. This significantly improves upon the previous state-of-the-art black-box methods for generating jailbreaks while using a smaller number of queries than them. Furthermore, TAP is also capable of jailbreaking LLMs protected by state-of-the-art guardrails, e.g., LlamaGuard.

cs.LG↗

arXiv2024

Smaller Confidence Intervals From IPW Estimators via Data-Dependent Coarsening

Inverse propensity-score weighted (IPW) estimators are prevalent in causal inference for estimating average treatment effects in observational studies. Under unconfoundedness, given accurate propensity scores and $n$ samples, the size of confidence intervals of IPW estimators scales down with $n$, and, several of their variants improve the rate of scaling. However, neither IPW estimators nor their variants are robust to inaccuracies: even if a single covariate has an $\varepsilon>0$ additive error in the propensity score, the size of confidence intervals of these estimators can increase arbitrarily. Moreover, even without errors, the rate with which the confidence intervals of these estimators go to zero with $n$ can be arbitrarily slow in the presence of extreme propensity scores (those close to 0 or 1). We introduce a family of Coarse IPW (CIPW) estimators that captures existing IPW estimators and their variants. Each CIPW estimator is an IPW estimator on a coarsened covariate space, where certain covariates are merged. Under mild assumptions, e.g., Lipschitzness in expected outcomes and sparsity of extreme propensity scores, we give an efficient algorithm to find a robust estimator: given $\varepsilon$-inaccurate propensity scores and $n$ samples, its confidence interval size scales with $\varepsilon+1/\sqrt{n}$. In contrast, under the same assumptions, existing estimators' confidence interval sizes are $Ω(1)$ irrespective of $\varepsilon$ and $n$. Crucially, our estimator is data-dependent and we show that no data-independent CIPW estimator can be robust to inaccuracies.

stat.ME↗

arXiv2024

Fair Classification with Partial Feedback: An Exploration-Based Data Collection Approach

In many predictive contexts (e.g., credit lending), true outcomes are only observed for samples that were positively classified in the past. These past observations, in turn, form training datasets for classifiers that make future predictions. However, such training datasets lack information about the outcomes of samples that were (incorrectly) negatively classified in the past and can lead to erroneous classifiers. We present an approach that trains a classifier using available data and comes with a family of exploration strategies to collect outcome data about subpopulations that otherwise would have been ignored. For any exploration strategy, the approach comes with guarantees that (1) all sub-populations are explored, (2) the fraction of false positives is bounded, and (3) the trained classifier converges to a ``desired'' classifier. The right exploration strategy is context-dependent; it can be chosen to improve learning guarantees and encode context-specific group fairness properties. Evaluation on real-world datasets shows that this approach consistently boosts the quality of collected outcome data and improves the fraction of true positives for all groups, with only a small reduction in predictive utility.

cs.LG↗

arXiv2023

Bias in Evaluation Processes: An Optimization-Based Model

Biases with respect to socially-salient attributes of individuals have been well documented in evaluation processes used in settings such as admissions and hiring. We view such an evaluation process as a transformation of a distribution of the true utility of an individual for a task to an observed distribution and model it as a solution to a loss minimization problem subject to an information constraint. Our model has two parameters that have been identified as factors leading to biases: the resource-information trade-off parameter in the information constraint and the risk-averseness parameter in the loss function. We characterize the distributions that arise from our model and study the effect of the parameters on the observed distribution. The outputs of our model enrich the class of distributions that can be used to capture variation across groups in the observed evaluations. We empirically validate our model by fitting real-world datasets and use it to study the effect of interventions in a downstream selection task. These results contribute to an understanding of the emergence of bias in evaluation processes and provide tools to guide the deployment of interventions to mitigate biases.

cs.CY↗

arXiv2023

Sampling Individually-Fair Rankings that are Always Group Fair

Rankings on online platforms help their end-users find the relevant information -- people, news, media, and products -- quickly. Fair ranking tasks, which ask to rank a set of items to maximize utility subject to satisfying group-fairness constraints, have gained significant interest in the Algorithmic Fairness, Information Retrieval, and Machine Learning literature. Recent works, however, identify uncertainty in the utilities of items as a primary cause of unfairness and propose introducing randomness in the output. This randomness is carefully chosen to guarantee an adequate representation of each item (while accounting for the uncertainty). However, due to this randomness, the output rankings may violate group fairness constraints. We give an efficient algorithm that samples rankings from an individually-fair distribution while ensuring that every output ranking is group fair. The expected utility of the output ranking is at least $α$ times the utility of the optimal fair solution. Here, $α$ depends on the utilities, position-discounts, and constraints -- it approaches 1 as the range of utilities or the position-discounts shrinks, or when utilities satisfy distributional assumptions. Empirically, we observe that our algorithm achieves individual and group fairness and that Pareto dominates the state-of-the-art baselines.

cs.CY↗

arXiv2023

Subset Selection Based On Multiple Rankings in the Presence of Bias: Effectiveness of Fairness Constraints for Multiwinner Voting Score Functions

We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest ``quality'' subset. Score functions from the multiwinner voting literature have been used to aggregate rankings into quality scores for subsets. We study this setting of subset selection problems when, in addition, rankings may contain systemic or unconscious biases toward a group of items. For a general model of input rankings and biases, we show that requiring the selected subset to satisfy group fairness constraints can improve the quality of the selection with respect to unbiased rankings. Importantly, we show that for fairness constraints to be effective, different multiwinner score functions may require a drastically different number of rankings: While for some functions, fairness constraints need an exponential number of rankings to recover a close-to-optimal solution, for others, this dependency is only polynomial. This result relies on a novel notion of ``smoothness'' of submodular functions in this setting that quantifies how well a function can ``correctly'' assess the quality of items in the presence of bias. The results in this paper can be used to guide the choice of multiwinner score functions for the subset selection setting considered here; we additionally provide a tool to empirically enable this.

cs.CY↗

arXiv2023

Maximizing Submodular Functions for Recommendation in the Presence of Biases

Subset selection tasks, arise in recommendation systems and search engines and ask to select a subset of items that maximize the value for the user. The values of subsets often display diminishing returns, and hence, submodular functions have been used to model them. If the inputs defining the submodular function are known, then existing algorithms can be used. In many applications, however, inputs have been observed to have social biases that reduce the utility of the output subset. Hence, interventions to improve the utility are desired. Prior works focus on maximizing linear functions -- a special case of submodular functions -- and show that fairness constraint-based interventions can not only ensure proportional representation but also achieve near-optimal utility in the presence of biases. We study the maximization of a family of submodular functions that capture functions arising in the aforementioned applications. Our first result is that, unlike linear functions, constraint-based interventions cannot guarantee any constant fraction of the optimal utility for this family of submodular functions. Our second result is an algorithm for submodular maximization. The algorithm provably outputs subsets that have near-optimal utility for this family under mild assumptions and that proportionally represent items from each group. In empirical evaluation, with both synthetic and real-world data, we observe that this algorithm improves the utility of the output subset for this family of submodular functions over baselines.

cs.LG↗

arXiv2022

Fair Ranking with Noisy Protected Attributes

The fair-ranking problem, which asks to rank a given set of items to maximize utility subject to group fairness constraints, has received attention in the fairness, information retrieval, and machine learning literature. Recent works, however, observe that errors in socially-salient (including protected) attributes of items can significantly undermine fairness guarantees of existing fair-ranking algorithms and raise the problem of mitigating the effect of such errors. We study the fair-ranking problem under a model where socially-salient attributes of items are randomly and independently perturbed. We present a fair-ranking framework that incorporates group fairness requirements along with probabilistic information about perturbations in socially-salient attributes. We provide provable guarantees on the fairness and utility attainable by our framework and show that it is information-theoretically impossible to significantly beat these guarantees. Our framework works for multiple non-disjoint attributes and a general class of fairness constraints that includes proportional and equal representation. Empirically, we observe that, compared to baselines, our algorithm outputs rankings with higher fairness, and has a similar or better fairness-utility trade-off compared to baselines.

cs.LG↗

arXiv2022

Fairness for AUC via Feature Augmentation

We study fairness in the context of classification where the performance is measured by the area under the curve (AUC) of the receiver operating characteristic. AUC is commonly used to measure the performance of prediction models. The same classifier can have significantly varying AUCs for different protected groups and, in real-world applications, it is often desirable to reduce such cross-group differences. We address the problem of how to acquire additional features to most greatly improve AUC for the disadvantaged group. We develop a novel approach, fairAUC, based on feature augmentation (adding features) to mitigate bias between identifiable groups. The approach requires only a few summary statistics to offer provable guarantees on AUC improvement, and allows managers flexibility in determining where in the fairness-accuracy tradeoff they would like to be. We evaluate fairAUC on synthetic and real-world datasets and find that it significantly improves AUC for the disadvantaged group relative to benchmarks maximizing overall AUC and minimizing bias between groups.

cs.LG↗

arXiv2022

Selection in the Presence of Implicit Bias: The Advantage of Intersectional Constraints

In selection processes such as hiring, promotion, and college admissions, implicit bias toward socially-salient attributes such as race, gender, or sexual orientation of candidates is known to produce persistent inequality and reduce aggregate utility for the decision maker. Interventions such as the Rooney Rule and its generalizations, which require the decision maker to select at least a specified number of individuals from each affected group, have been proposed to mitigate the adverse effects of implicit bias in selection. Recent works have established that such lower-bound constraints can be very effective in improving aggregate utility in the case when each individual belongs to at most one affected group. However, in several settings, individuals may belong to multiple affected groups and, consequently, face more extreme implicit bias due to this intersectionality. We consider independently drawn utilities and show that, in the intersectional case, the aforementioned non-intersectional constraints can only recover part of the total utility achievable in the absence of implicit bias. On the other hand, we show that if one includes appropriate lower-bound constraints on the intersections, almost all the utility achievable in the absence of implicit bias can be recovered. Thus, intersectional constraints can offer a significant advantage over a reductionist dimension-by-dimension non-intersectional approach to reducing inequality.

cs.CY↗

arXiv2021

Fair Classification with Adversarial Perturbations

We study fair classification in the presence of an omniscient adversary that, given an $η$, is allowed to choose an arbitrary $η$-fraction of the training samples and arbitrarily perturb their protected attributes. The motivation comes from settings in which protected attributes can be incorrect due to strategic misreporting, malicious actors, or errors in imputation; and prior approaches that make stochastic or independence assumptions on errors may not satisfy their guarantees in this adversarial setting. Our main contribution is an optimization framework to learn fair classifiers in this adversarial setting that comes with provable guarantees on accuracy and fairness. Our framework works with multiple and non-binary protected attributes, is designed for the large class of linear-fractional fairness metrics, and can also handle perturbations besides protected attributes. We prove near-tightness of our framework's guarantees for natural hypothesis classes: no algorithm can have significantly better accuracy and any algorithm with better fairness must have lower accuracy. Empirically, we evaluate the classifiers produced by our framework for statistical rate on real-world and synthetic datasets for a family of adversaries.

cs.LG↗

arXiv2021

Input Validation with Symbolic Execution

Symbolic execution has always been plagued by the inability to handle programs that require highly structured inputs. Most often, the symbolic execution engine gets overwhelmed by the sheer number of infeasible paths and fails to explore enough feasible paths to gain any respectable coverage. In this paper, we propose a system, InVaSion, that attempts to solve this problem for forking-based symbolic execution engines. We propose an input specification language (ISL) that is based on a finite-state automaton but includes guarded transitions, a set of registers and a set of commands to update the register states. We demonstrate that our language is expressive enough to handle complex input specifications, like the Tiff image format, while not requiring substantial human effort; even the Tiff image specification could be specified in our language with an automaton of about 35 states. InVaSion translates the given program and the input specification into a non-deterministic program and uses symbolic execution to instantiate the non-determinism. This allows our tool to work with any forking-based symbolic execution engine and with no requirement of any special theory solver. Over our set of benchmarks, on an average, InVaSion was able to increase branch coverage from 24.97% to 67.84% over baseline KLEE.

cs.PL↗

arXiv2021

Mitigating Bias in Set Selection with Noisy Protected Attributes

Subset selection algorithms are ubiquitous in AI-driven applications, including, online recruiting portals and image search engines, so it is imperative that these tools are not discriminatory on the basis of protected attributes such as gender or race. Currently, fair subset selection algorithms assume that the protected attributes are known as part of the dataset. However, protected attributes may be noisy due to errors during data collection or if they are imputed (as is often the case in real-world settings). While a wide body of work addresses the effect of noise on the performance of machine learning algorithms, its effect on fairness remains largely unexamined. We find that in the presence of noisy protected attributes, in attempting to increase fairness without considering noise, one can, in fact, decrease the fairness of the result! Towards addressing this, we consider an existing noise model in which there is probabilistic information about the protected attributes (e.g., [58, 34, 20, 46]), and ask is fair selection possible under noisy conditions? We formulate a ``denoised'' selection problem which functions for a large class of fairness metrics; given the desired fairness goal, the solution to the denoised problem violates the goal by at most a small multiplicative amount with high probability. Although this denoised problem turns out to be NP-hard, we give a linear-programming based approximation algorithm for it. We evaluate this approach on both synthetic and real-world datasets. Our empirical results show that this approach can produce subsets which significantly improve the fairness metrics despite the presence of noisy protected attributes, and, compared to prior noise-oblivious approaches, has better Pareto-tradeoffs between utility and fairness.

cs.CY↗

arXiv2020

The Effect of the Rooney Rule on Implicit Bias in the Long Term

A robust body of evidence demonstrates the adverse effects of implicit bias in various contexts--from hiring to health care. The Rooney Rule is an intervention developed to counter implicit bias and has been implemented in the private and public sectors. The Rooney Rule requires that a selection panel include at least one candidate from an underrepresented group in their shortlist of candidates. Recently, Kleinberg and Raghavan proposed a model of implicit bias and studied the effectiveness of the Rooney Rule when applied to a single selection decision. However, selection decisions often occur repeatedly over time. Further, it has been observed that, given consistent counterstereotypical feedback, implicit biases against underrepresented candidates can change. We consider a model of how a selection panel's implicit bias changes over time given their hiring decisions either with or without the Rooney Rule in place. Our main result is that, when the panel is constrained by the Rooney Rule, their implicit bias roughly reduces at a rate that is the inverse of the size of the shortlist--independent of the number of candidates, whereas without the Rooney Rule, the rate is inversely proportional to the number of candidates. Thus, when the number of candidates is much larger than the size of the shortlist, the Rooney Rule enables a faster reduction in implicit bias, providing an additional reason in favor of using it as a strategy to mitigate implicit bias. Towards empirically evaluating the long-term effect of the Rooney Rule in repeated selection decisions, we conduct an iterative candidate selection experiment on Amazon MTurk. We observe that, indeed, decision-makers subject to the Rooney Rule select more minority candidates in addition to those required by the rule itself than they would if no rule is in effect, and do so without considerably decreasing the utility of candidates selected.

cs.CY↗

arXiv2020

Two Player Hidden Pointer Chasing and Multi-Pass Lower Bounds in Turnstile Streams

The authors have withdrawn this paper due to an error in the proof of Lemma 3.4. -------------------------------------------------------------------------------------------- The authors have withdrawn this paper due to an error in the proof of Lemma 3.4z(Assadi, Chen, and Khanna, 2019) define a 4-player hidden-pointer-chasing ($\mathsf{HPC}^4$), and using it, give strong multi-pass lower bounds for graph problems in the streaming model of computation and a lower bound on the query complexity of sub-modular minimization. We present a two-player version ($\mathsf{HPC}^2$) of $\mathsf{HPC}^4$ that has matching communication complexity to $\mathsf{HPC}^4$. Our formulation allows us to lower bound its communication complexity with a simple direct-sum argument. Using this lower bound on the communication complexity of $\mathsf{HPC}^2$, we retain the streaming and query complexity lower bounds by (Assadi, Chen, and Khanna, 2019). Further, by giving reductions from $\mathsf{HPC}^2$, we prove new multi-pass space lower bounds for graph problems in turnstile streams. In particular, we show that any algorithm which computes the exact weight of the maximum weighted matching in an $n$-vertex graph requires $\tilde{O}(n^{2})$ space unless it makes $ω(\log n)$ passes over the turnstile stream, and that any algorithm which computes the minimum $s\text{-}t$ distance in an $n$-vertex graph requires $n^{2-o(1)}$ space unless it makes $n^{Ω(1)}$ passes over the turnstile stream. Our reductions can be modified to use $\mathsf{HPC}^4$ as well.

cs.CC↗

arXiv2020

Interventions for Ranking in the Presence of Implicit Bias

Implicit bias is the unconscious attribution of particular qualities (or lack thereof) to a member from a particular social group (e.g., defined by gender or race). Studies on implicit bias have shown that these unconscious stereotypes can have adverse outcomes in various social contexts, such as job screening, teaching, or policing. Recently, (Kleinberg and Raghavan, 2018) considered a mathematical model for implicit bias and showed the effectiveness of the Rooney Rule as a constraint to improve the utility of the outcome for certain cases of the subset selection problem. Here we study the problem of designing interventions for the generalization of subset selection -- ranking -- that requires to output an ordered set and is a central primitive in various social and computational contexts. We present a family of simple and interpretable constraints and show that they can optimally mitigate implicit bias for a generalization of the model studied in (Kleinberg and Raghavan, 2018). Subsequently, we prove that under natural distributional assumptions on the utilities of items, simple, Rooney Rule-like, constraints can also surprisingly recover almost all the utility lost due to implicit biases. Finally, we augment our theoretical results with empirical findings on real-world distributions from the IIT-JEE (2009) dataset and the Semantic Scholar Research corpus.

cs.CY↗