arXiv subjects

Yash Pote

Publications and source records attributed to Yash Pote.

14 recordsLinked to original sources

arXiv2026

Entropy Equivalence Testing

We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given samples from two unknown distributions $p,q$ and a parameter $\varepsilon \in(0,1/2]$, between $p=q$ and $|H(p)-H(q)| \geq \varepsilon$ (where $H$ denotes the Shannon entropy). We provide a time- and sample-efficient algorithm for this task, showing that the optimal sample complexity for this task can be significantly lower than that of closeness testing. As an application, we leverage this result to provide the first non-trivial testing algorithm for (standard) closeness of low-degree \emph{Bayesian networks}, which significantly improves on either the sample or time complexity of a baseline based on full learning.

cs.DS↗

arXiv2025

A Distribution Testing Approach to Clustering Distributions

We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters are $\varepsilon$-far in total variation, the goal is to recover the partition. We establish upper and lower bounds on the sample complexity for two fundamental cases: (1) when one of the cluster's distributions is known, and (2) when both are unknown. Our upper and lower bounds characterize the sample complexity's dependence on the domain size $n$, number of distributions $k$, size $r$ of one of the clusters, and distance $\varepsilon$. In particular, we achieve tightness with respect to $(n,k,r,\varepsilon)$ (up to an $O(\log k)$ factor) for all regimes.

cs.DS↗

arXiv2025

Instance Dependent Testing of Samplers using Interval Conditioning

Sampling algorithms play a pivotal role in probabilistic AI. However, verifying if a sampler program indeed samples from the claimed distribution is a notoriously hard problem. Provably correct testers like Barbarik, Teq, Flash, CubeProbe for testing of different kinds of samplers were proposed only in the last few years. All these testers focus on the worst-case efficiency, and do not support verification of samplers over infinite domains, a case occurring frequently in Astronomy, Finance, Network Security, etc. In this work, we design the first tester of samplers with instance-dependent efficiency, allowing us to test samplers over natural numbers. Our tests are developed via a novel distance estimation algorithm between an unknown and a known probability distribution using an interval conditioning framework. The core technical contribution is a new connection with probability mass estimation of a continuous distribution. The practical gains are also substantial: our experiments establish up to 1000x speedup over state-of-the-art testers.

cs.DS↗

arXiv2025

Zero-Shot Attribution for Large Language Models: A Distribution Testing Approach

A growing fraction of all code is sampled from Large Language Models (LLMs). We investigate the problem of attributing code generated by language models using hypothesis testing to leverage established techniques and guarantees. Given a set of samples $S$ and a suspect model $\mathcal{L}^*$, our goal is to assess the likelihood of $S$ originating from $\mathcal{L}^*$. Due to the curse of dimensionality, this is intractable when only samples from the LLM are given: to circumvent this, we use both samples and density estimates from the LLM, a form of access commonly available. We introduce $\mathsf{Anubis}$, a zero-shot attribution tool that frames attribution as a distribution testing problem. Our experiments on a benchmark of code samples show that $\mathsf{Anubis}$ achieves high AUROC scores ( $\ge0.9$) when distinguishing between LLMs like DeepSeek-Coder, CodeGemma, and Stable-Code using only $\approx 2000$ samples.

cs.LG↗

arXiv2025

Learning Probabilistic Temporal Logic Specifications for Stochastic Systems

There has been substantial progress in the inference of formal behavioural specifications from sample trajectories, for example, using Linear Temporal Logic (LTL). However, these techniques cannot handle specifications that correctly characterise systems with stochastic behaviour, which occur commonly in reinforcement learning and formal verification. We consider the passive learning problem of inferring a Boolean combination of probabilistic LTL (PLTL) formulas from a set of Markov chains, classified as either positive or negative. We propose a novel learning algorithm that infers concise PLTL specifications, leveraging grammar-based enumeration, search heuristics, probabilistic model checking and Boolean set-cover procedures. We demonstrate the effectiveness of our algorithm in two use cases: learning from policies induced by RL algorithms and learning from variants of a probabilistic model. In both cases, our method automatically and efficiently extracts PLTL specifications that succinctly characterise the temporal differences between the policies or model variants.

cs.LO↗

arXiv2023

Testing Self-Reducible Samplers

Samplers are the backbone of the implementations of any randomised algorithm. Unfortunately, obtaining an efficient algorithm to test the correctness of samplers is very hard to find. Recently, in a series of works, testers like $\mathsf{Barbarik}$, $\mathsf{Teq}$, $\mathsf{Flash}$ for testing of some particular kinds of samplers, like CNF-samplers and Horn-samplers, were obtained. But their techniques have a significant limitation because one can not expect to use their methods to test for other samplers, such as perfect matching samplers or samplers for sampling linear extensions in posets. In this paper, we present a new testing algorithm that works for such samplers and can estimate the distance of a new sampler from a known sampler (say, uniform sampler). Testing the identity of distributions is the heart of testing the correctness of samplers. This paper's main technical contribution is developing a new distance estimation algorithm for distributions over high-dimensional cubes using the recently proposed sub-cube conditioning sampling model. Given subcube conditioning access to an unknown distribution $P$, and a known distribution $Q$ defined over $\{0,1\}^n$, our algorithm $\mathsf{CubeProbeEst}$ estimates the variation distance between $P$ and $Q$ within additive error $\zeta$ using $O\left({n^2}/{\zeta^4}\right)$ subcube conditional samples from $P$. Following the testing-via-learning paradigm, we also get a tester which distinguishes between the cases when $P$ and $Q$ are $\varepsilon$-close or $\eta$-far in variation distance with probability at least $0.99$ using $O({n^2}/{(\eta-\varepsilon)^4})$ subcube conditional samples. The estimation algorithm in the sub-cube conditioning sampling model helps us to design the first tester for self-reducible samplers.

cs.DS↗

arXiv2023

Distance Estimation for High-Dimensional Discrete Distributions

Given two distributions $\mathcal{P}$ and $\mathcal{Q}$ over a high-dimensional domain $\{0,1\}^n$, and a parameter $\varepsilon$, the goal of distance estimation is to determine the statistical distance between $\mathcal{P}$ and $\mathcal{Q}$, up to an additive tolerance $\pm \varepsilon$. Since exponential lower bounds (in $n$) are known for the problem in the standard sampling model, research has focused on richer query models where one can draw conditional samples. This paper presents the first polynomial query distance estimator in the conditional sampling model ($\mathsf{COND}$). We base our algorithm on the relatively weaker \textit{subcube conditional} sampling ($\mathsf{SUBCOND}$) oracle, which draws samples from the distribution conditioned on some of the dimensions. $\mathsf{SUBCOND}$ is a promising model for widespread practical use because it captures the natural behavior of discrete samplers. Our algorithm makes $\tilde{\mathcal{O}}(n^3/\varepsilon^5)$ queries to $\mathsf{SUBCOND}$.

cs.DS↗

arXiv2023

On Scalable Testing of Samplers

In this paper we study the problem of testing of constrained samplers over high-dimensional distributions with $(\varepsilon,\eta,\delta)$ guarantees. Samplers are increasingly used in a wide range of safety-critical ML applications, and hence the testing problem has gained importance. For $n$-dimensional distributions, the existing state-of-the-art algorithm, $\mathsf{Barbarik2}$, has a worst case query complexity of exponential in $n$ and hence is not ideal for use in practice. Our primary contribution is an exponentially faster algorithm that has a query complexity linear in $n$ and hence can easily scale to larger instances. We demonstrate our claim by implementing our algorithm and then comparing it against $\mathsf{Barbarik2}$. Our experiments on the samplers $\mathsf{wUnigen3}$ and $\mathsf{wSTS}$, find that $\mathsf{Barbarik3}$ requires $10\times$ fewer samples for $\mathsf{wUnigen3}$ and $450\times$ fewer samples for $\mathsf{wSTS}$ as compared to $\mathsf{Barbarik2}$.

cs.DS↗

arXiv2022

Efficiently Enabling Block Semantics and Data Updates in DNA Storage

We propose a novel and flexible DNA-storage architecture, which divides the storage space into fixed-size units (blocks) that can be independently and efficiently accessed at random for both read and write operations, and further allows efficient sequential access to consecutive data blocks. In contrast to prior work, in our architecture a pair of random-access PCR primers of length 20 does not define a single object, but an independent storage partition, which is internally blocked and managed independently of other partitions. We expose the flexibility and constraints with which the internal address space of each partition can be managed, and incorporate them into our design to provide rich and functional storage semantics, such as block-storage organization, efficient implementation of data updates, and sequential access. To leverage the full power of the prefix-based nature of PCR addressing, we define a methodology for transforming the internal addressing scheme of a partition into an equivalent that is PCR-compatible. This allows us to run PCR with primers that can be variably elongated to include a desired part of the internal address, and thus narrow down the scope of the reaction to retrieve a specific block or a range of blocks within the partition with sufficiently high accuracy. Our wetlab evaluation demonstrates the practicality of the proposed ideas and a 140x reduction in sequencing cost and latency for retrieval of individual blocks within the partition.

cs.ET↗

arXiv2022

Managing Reliability Skew in DNA Storage

DNA is emerging as an increasingly attractive medium for data storage due to a number of important and unique advantages it offers, most notably the unprecedented durability and density. While the technology is evolving rapidly, the prohibitive cost of reads and writes, the high frequency and the peculiar nature of errors occurring in DNA storage pose a significant challenge to its adoption. In this work we make a novel observation that the probability of successful recovery of a given bit from any type of a DNA-based storage system highly depends on its physical location within the DNA molecule. In other words, when used as a storage medium, some parts of DNA molecules appear significantly more reliable than others. We show that large differences in reliability between different parts of DNA molecules lead to highly inefficient use of error-correction resources, and that commonly used techniques such as unequal error-correction cannot be used to bridge the reliability gap between different locations in the context of DNA storage. We then propose two approaches to address the problem. The first approach is general and applies to any types of data; it stripes the data and ECC codewords across DNA molecules in a particular fashion such that the effects of errors are spread out evenly across different codewords and molecules, effectively de-biasing the underlying storage medium. The second approach is application-specific, and seeks to leverage the underlying reliability bias by using application-aware mapping of data onto DNA molecules such that data that requires higher reliability is stored in more reliable locations, whereas data that needs lower reliability is stored in less reliable parts of DNA molecules. We show that the proposed data mapping can be used to achieve graceful degradation in the presence of high error rates, or to implement the concept of approximate storage in DNA.

cs.ET↗

arXiv2021

Testing Probabilistic Circuits

Probabilistic circuits (PCs) are a powerful modeling framework for representing tractable probability distributions over combinatorial spaces. In machine learning and probabilistic programming, one is often interested in understanding whether the distributions learned using PCs are close to the desired distribution. Thus, given two probabilistic circuits, a fundamental problem of interest is to determine whether their distributions are close to each other. The primary contribution of this paper is a closeness test for PCs with respect to the total variation distance metric. Our algorithm utilizes two common PC queries, counting and sampling. In particular, we provide a poly-time probabilistic algorithm to check the closeness of two PCs when the PCs support tractable approximate counting and sampling. We demonstrate the practical efficiency of our algorithmic framework via a detailed experimental evaluation of a prototype implementation against a set of 475 PC benchmarks. We find that our test correctly decides the closeness of all 475 PCs within 3600 seconds.

cs.DS↗

arXiv2021

Partition Function Estimation: A Quantitative Study

Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its computation is key to several probabilistic reasoning tasks. Given the #P-hardness of computing the partition function, several techniques have been proposed over the years with varying guarantees on the quality of estimates and their runtime behavior. This paper seeks to present a survey of 18 techniques and a rigorous empirical study of their behavior across an extensive set of benchmarks. Our empirical study draws up a surprising observation: exact techniques are as efficient as the approximate ones, and therefore, we conclude with an optimistic view of opportunities for the design of approximate techniques with enhanced scalability. Motivated by the observation of an order of magnitude difference between the Virtual Best Solver and the best performing tool, we envision an exciting line of research focused on the development of portfolio solvers.

cs.AI↗

arXiv2020

On Testing of Samplers

Given a set of items $\mathcal{F}$ and a weight function $\mathtt{wt}: \mathcal{F} \mapsto (0,1)$, the problem of sampling seeks to sample an item proportional to its weight. Sampling is a fundamental problem in machine learning. The daunting computational complexity of sampling with formal guarantees leads designers to propose heuristics-based techniques for which no rigorous theoretical analysis exists to quantify the quality of generated distributions. This poses a challenge in designing a testing methodology to test whether a sampler under test generates samples according to a given distribution. Only recently, Chakraborty and Meel (2019) designed the first scalable verifier, called Barbarik1, for samplers in the special case when the weight function $\mathtt{wt}$ is constant, that is, when the sampler is supposed to sample uniformly from $\mathcal{F}$ . The techniques in Barbarik1, however, fail to handle general weight functions. The primary contribution of this paper is an affirmative answer to the above challenge: motivated by Barbarik1 but using different techniques and analysis, we design Barbarik2 an algorithm to test whether the distribution generated by a sampler is $\varepsilon$-close or $η$-far from any target distribution. In contrast to black-box sampling techniques that require a number of samples proportional to $|\mathcal{F}|$ , Barbarik2 requires only $\tilde{O}(tilt(\mathtt{wt},φ)^2/η(η- 6\varepsilon)^3)$ samples, where the $tilt$ is the maximum ratio of weights of two satisfying assignments. Barbarik2 can handle any arbitrary weight function. We present a prototype implementation of Barbarik2 and use it to test three state-of-the-art samplers.

cs.DS↗

arXiv2019

Phase Transition Behavior of Cardinality and XOR Constraints

The runtime performance of modern SAT solvers is deeply connected to the phase transition behavior of CNF formulas. While CNF solving has witnessed significant runtime improvement over the past two decades, the same does not hold for several other classes such as the conjunction of cardinality and XOR constraints, denoted as CARD-XOR formulas. The problem of determining the satisfiability of CARD-XOR formulas is a fundamental problem with a wide variety of applications ranging from discrete integration in the field of artificial intelligence to maximum likelihood decoding in coding theory. The runtime behavior of random CARD-XOR formulas is unexplored in prior work. In this paper, we present the first rigorous empirical study to characterize the runtime behavior of 1-CARD-XOR formulas. We show empirical evidence of a surprising phase-transition that follows a non-linear tradeoff between CARD and XOR constraints.

cs.AI↗