Related papers: Testing exchangeability: fork-convexity, supermart…
We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…
Given a graph where every vertex has exactly one labeled token, how can we most quickly execute a given permutation on the tokens? In (sequential) token swapping, the goal is to use the shortest possible sequence of swaps, each of which…
We present a nonparametric prior over reversible Markov chains. We use completely random measures, specifically gamma processes, to construct a countably infinite graph with weighted edges. By enforcing symmetry to make the edges undirected…
Non-volatile memory (NVM), also known as persistent memory, is an emerging paradigm for memory that preserves its contents even after power loss. NVM is widely expected to become ubiquitous, and hardware architectures are already providing…
Experimentation involves risk. The investigator expends time and money in the pursuit of data that supports a hypothesis. In the end, the investigator may find that all of these costs were for naught and the data fail to reject the null.…
We study the problem of designing consistent sequential two-sample tests in a nonparametric setting. Guided by the principle of testing by betting, we reframe this task into that of selecting a sequence of payoff functions that maximize the…
In scientific studies involving analyses of multivariate data, basic but important questions often arise for the researcher: Is the sample exchangeable, meaning that the joint distribution of the sample is invariant to the ordering of the…
Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper…
Multiplicative stochasticity such as Dropout improves the robustness and generalizability of deep neural networks. Here, we further demonstrate that always-on multiplicative stochasticity combined with simple threshold neurons are…
We propose two nonparametric tests for investigating the pathwise properties of a signal modeled as the sum of a L\'{e}vy process and a Brownian semimartingale. Using a nonparametric threshold estimator for the continuous component of the…
It is a well-known fact that an exchangeable sequence has empirical distributions that form a reverse-martingale. This paper is devoted to proof of the converse statement. As a byproduct of the proof for the binary case, we introduce and…
In this paper we propose a computationally efficient multiple hypothesis testing procedure for persistent homology. The computational efficiency of our procedure is based on the observation that one can empirically simulate a null…
We study finite-horizon optimal switching with discrete intervention dates on a general filtration, allowing continuous-time observations between decision dates, and develop a deep-learning-based dual framework with computable upper bounds.…
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
A martingale framework for concept change detection based on testing data exchangeability was recently proposed (Ho, 2005). In this paper, we describe the proposed change-detection test based on the Doob's Maximal Inequality and show that…
In 1976, Lai constructed a nontrivial confidence sequence for the mean $\mu$ of a Gaussian distribution with unknown variance $\sigma^2$. Curiously, he employed both an improper (right Haar) mixture over $\sigma$ and an improper (flat)…
We explore the class of exchangeable Bernoulli distributions building on their geometrical structure. Exchangeable Bernoulli probability mass functions are points in a convex polytope and we have found analytical expressions for their…
Let A be a standard Borel space, and consider the space A^{\bbN^{(k)}} of A-valued arrays indexed by all size-k subsets of \bbN. This paper concerns random measures on such a space whose laws are invariant under the natural action of…
We study safety verification for multithreaded programs with recursive parallelism (i.e. unbounded thread creation and recursion) as well as unbounded integer variables. Since the threads in each program configuration are structured in a…
Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…