Related papers: Distribution of complexities in the Vai script
Tree-based priors for probability distributions are usually specified using a predetermined, data-independent collection of candidate recursive partitions of the sample space. To characterize an unknown target density in detail over the…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…
We propose a Bayesian distributionally robust variational inequality (DRVI) framework that models the data-generating distribution through a finite mixture family, which allows us to study the DRVI on a tractable finite-dimensional…
This paper presents a variant of the Multinomial mixture model tailored to the unsupervised classification of short text data. While the Multinomial probability vector is traditionally assigned a Dirichlet prior distribution, this work…
The first step in statistical reliability studies of coherent systems is the estimation of the reliability of each system component. For the cases of parallel and series systems the literature is abundant. It seems that the present paper is…
We study the Poisson Boolean model where the grains are random convex bodies with a rotation-invariant distribution. We say that a grain distribution is dense if the union of the grains covers the entire space and robust if the union of the…
We consider the problems of robust PAC learning from distributed and streaming data, which may contain malicious errors and outliers, and analyze their fundamental complexity questions. In particular, we establish lower bounds on the…
We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a Beta Process. It also…
We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a…
We study the structure of satisfying assignments of a random 3-SAT formula. In particular, we show that a random formula of density 4.453 or higher almost surely has no non-trivial "core" assignments. Core assignments are certain partial…
Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL)…
Given a parametric polynomial curve $\gamma:[a,b]\rightarrow \mathbb{R}^n$, how can we sample a random point $\mathfrak{x}\in \mathrm{im}(\gamma)$ in such a way that it is distributed uniformly with respect to the arc-length? Unfortunately,…
Bayesian inference for spatial point patterns is often hindered computationally by intractable likelihoods. In the frequentist literature, estimating equations utilizing pseudolikelihoods have long been used for simulation-free parameter…
While observational data are routinely used to estimate causal effects of biomedical treatments, doing so requires special methods to adjust for observed confounding. These methods invariably rely on untestable statistical and causal…
A connection between integrability properties and general statistical properties of the spectra of symmetric transfer matrices of the asymmetric eight-vertex model is studied using random matrix theory (eigenvalue spacing distribution and…
Time series classification is an important problem in real world. Due to its non-stationary property that the distribution changes over time, it remains challenging to build models for generalization to unseen distributions. In this paper,…
The structure of a Bayesian network encodes most of the information about the probability distribution of the data, which is uniquely identified given some general distributional assumptions. Therefore it's important to study the…
It is well-known that if a subset A of a finite Abelian group G satisfies a quasirandomness property called uniformity of degree k, then it contains roughly the expected number of arithmetic progressions of length k, that is, the number of…
Preferential attachment is a popular generative mechanism to explain the widespread observation of power law distributed networks. We introduce an alternative explanation for the phenomenon by allowing the link growth rates to vary across…
A key problem in constrained random verification (CRV) concerns generation of input stimuli that result in good coverage of the system's runs in targeted corners of its behavior space. Existing CRV solutions however provide no formal…