Related papers: Improving Wald's (approximate) sequential probabil…
Stochastic gradient descent is a canonical tool for addressing stochastic optimization problems, and forms the bedrock of modern machine learning and statistics. In this work, we seek to balance the fact that attenuating step-size is…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
Testing whether a variable of interest affects the outcome is one of the most fundamental problem in statistics and is often the main scientific question of interest. To tackle this problem, the conditional randomization test (CRT) is…
Soft Prompt Tuning (SPT) is a parameter-efficient method for adapting pre-trained language models (PLMs) to specific tasks by inserting learnable embeddings, or soft prompts, at the input layer of the PLM, without modifying its parameters.…
Responding appropriately to the detections of a sequential change detector requires knowledge of the rate at which false positives occur in the absence of change. Setting detection thresholds to achieve a desired false positive rate is…
Consider the problem of finding a population or a probability distribution amongst many with the largest mean when these means are unknown but population samples can be simulated or otherwise generated. Typically, by selecting largest…
Quantum computing promises polynomial and exponential speedups in many domains, such as unstructured search and prime number factoring. However, quantum programs yield probabilistic outputs from exponentially growing distributions and are…
We study population convergence guarantees of stochastic gradient descent (SGD) for smooth convex objectives in the interpolation regime, where the noise at optimum is zero or near zero. The behavior of the last iterate of SGD in this…
We study the sample complexity of the Sign-Perturbed Sums (SPS) method, which constructs exact, non-asymptotic confidence regions for the true system parameters under mild statistical assumptions, such as independent and symmetric noise…
We construct an asymptotic prediction interval for the population-wise error rate (PWER), which is a multiple type I error criterion for clinical trials with overlapping patient populations. The PWER is the probability that a randomly…
We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…
The satisfiability threshold for constraint satisfaction problems is that value of the ratio of constraints (or clauses) to variables, above which the probability that a random instance of the problem has a solution is zero in the large…
Scaling the amount of data used for supervied fine-tuning(SFT) does not guarantee the proportional gains in model performance, highlighting a critical need to understand what makes training samples effective. This work identifies two…
We propose a model for multiclass classification of time series to make a prediction as early and as accurate as possible. The matrix sequential probability ratio test (MSPRT) is known to be asymptotically optimal for this setting, but…
This paper introduces the sequential CRT, which is a variable selection procedure that combines the conditional randomization test (CRT) and Selective SeqStep+. Valid p-values are constructed via the flexible CRT, which are then ordered and…
The empirical Wasserstein projection (WP) distance quantifies the Wasserstein distance from the empirical distribution to a set of probability measures satisfying given expectation constraints. The WP is a powerful tool because it mitigates…
Large language models (LLMs) have achieved impressive results on multi-step mathematical reasoning, yet at the cost of high computational overhead. This challenge is particularly acute for test-time scaling methods such as parallel…
We establish the satisfiability threshold for random $k$-SAT for all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $\alpha_*(k)$ such that a random $k$-SAT formula of clause density $\alpha$ is with…
Predicting sets of outcomes -- instead of unique outcomes -- is a promising solution to uncertainty quantification in statistical learning. Despite a rich literature on constructing prediction sets with statistical guarantees, adapting to…
Due to the limited number of bits in floating-point or fixed-point arithmetic, rounding is a necessary step in many computations. Although rounding methods can be tailored for different applications, round-off errors are generally…