arXiv subjects

Rohan Chauhan

Publications and source records attributed to Rohan Chauhan.

3 recordsLinked to original sources

arXiv2026

Efficient Learning of Truncated Boolean Product Distributions: Influence to the Rescue

Learning the natural parameters $z \in \mathbb{R}^n$ of discrete distributions $\mu_z$ from independent samples constrained to a subset $S \subseteq \{0,1\}^n$ is a foundational challenge in high-dimensional statistics. Existing methods for efficiently estimating truncated Boolean product distributions, notably the work of [Fotakis et al' COLT'20, Algorithmica '22], require either strong local connectivity assumptions on $S$ -- a property denoted fatness -- or stringent anti-concentration assumptions and necessitate the total mass of the truncation set to be a constant with respect to $n$. Moreover, the results in [Fotakis et al' COLT'20, Algorithmica '22] suffer from sample complexities that scale as $\Omega(2^n)$ if the mass of $S$ is exponentially small in $n$. In this work, we circumvent these limitations by analyzing the geometry of $S$ under the measure $\mu_z$. We refine the existing parameter estimation guarantees under the fatness assumption, improving the prior sample complexity to $O( \log n / \epsilon^2)$ for $\ell_\infty$-recovery, matching the untruncated minimax rate. We further generalize fatness using the notion of influence utilized in the analysis of Boolean functions and provide sufficient conditions for efficient inference. Notably, unlike previous work, our method does not require sampling at arbitrary parameterizations of the model. Lastly, we establish a theoretical lower bound demonstrating the sample complexity exhibits an intrinsic exponential dependence on the width of the model and the minimum distance between elements in the set.

cs.LG↗

arXiv2026

On the Computational Complexity of Performative Prediction

Performative prediction captures the phenomenon where deploying a predictive model shifts the underlying data distribution. While simple retraining dynamics are known to converge linearly when the performative effects are weak ($\rho < 1$), the complexity in the regime $\rho > 1$ was hitherto open. In this paper, we establish a sharp phase transition: computing an $\epsilon$-performatively stable point is PPAD-complete -- and thus polynomial-time equivalent to Nash equilibria in general-sum games -- even when $\rho = 1 + O(\epsilon)$. This intractability persists even in the ostensibly simple setting with a quadratic loss function and linear distribution shifts. One of our key technical contributions is to extend this PPAD-hardness result to general convex domains, which is of broader interest in the complexity of variational inequalities. Finally, we address the special case of strategic classification, showing that computing a strategic local optimum is PLS-hard.

cs.LG↗

arXiv2025

Learning the Inverse Temperature of Ising Models under Hard Constraints using One Sample

We consider the problem of estimating inverse temperature parameter $\beta$ of an $n$-dimensional truncated Ising model using a single sample. Given a graph $G = (V,E)$ with $n$ vertices, a truncated Ising model is a probability distribution over the $n$-dimensional hypercube $\{-1,1\}^n$ where each configuration $\mathbf{\sigma}$ is constrained to lie in a truncation set $S \subseteq \{-1,1\}^n$ and has probability $\Pr(\mathbf{\sigma}) \propto \exp(\beta\mathbf{\sigma}^\top A\mathbf{\sigma})$ with $A$ being the adjacency matrix of $G$. We adopt the recent setting of [Galanis et al. SODA'24], where the truncation set $S$ can be expressed as the set of satisfying assignments of a $k$-SAT formula. Given a single sample $\mathbf{\sigma}$ from a truncated Ising model, with inverse parameter $\beta^*$, underlying graph $G$ of bounded degree $\Delta$ and $S$ being expressed as the set of satisfying assignments of a $k$-SAT formula, we design in nearly $O(n)$ time an estimator $\hat{\beta}$ that is $O(\Delta^3/\sqrt{n})$-consistent with the true parameter $\beta^*$ for $k \gtrsim \log(d^2k)\Delta^3.$ Our estimator is based on the maximization of the pseudolikelihood, a notion that has received extensive analysis for various probabilistic models without [Chatterjee, Annals of Statistics '07] or with truncation [Galanis et al. SODA '24]. Our approach generalizes recent techniques from [Daskalakis et al. STOC '19, Galanis et al. SODA '24], to confront the more challenging setting of the truncated Ising model.

cs.LG↗