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This paper studies the approximation and generalization abilities of score-based neural network generative models (SGMs) in estimating an unknown distribution $P_0$ from $n$ i.i.d. observations in $d$ dimensions. Assuming merely that $P_0$…
Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…
This paper is on Bayesian inference for parametric statistical models that are defined by a stochastic simulator which specifies how data is generated. Exact sampling is then possible but evaluating the likelihood function is typically…
We introduce Thurstonian Boltzmann Machines (TBM), a unified architecture that can naturally incorporate a wide range of data inputs at the same time. Our motivation rests in the Thurstonian view that many discrete data types can be…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
Restricted Boltzmann Machine (RBM) is a bipartite graphical model that is used as the building block in energy-based deep generative models. Due to numerical stability and quantifiability of the likelihood, RBM is commonly used with…
Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine, involves training a top-down directed generative model together with a bottom-up auxiliary…
The Bayesian network structure learning (BNSL) problem asks for a directed acyclic graph that maximizes a given score function. For networks with $n$ nodes, the fastest known algorithms run in time $O(2^n n^2)$ in the worst case, with no…
Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used…
We explore the theoretical and numerical property of a fully Bayesian model selection method in sparse ultrahigh-dimensional settings, i.e., $p\gg n$, where $p$ is the number of covariates and $n$ is the sample size. Our method consists of…
Boolean-width is a recently introduced graph parameter. Many problems are fixed parameter tractable when parametrized by boolean-width, for instance "Minimum Weighted Dominating Set" (MWDS) problem can be solved in $O^*(2^{3k})$ time given…
We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n 2^n) time,…
Complicated generative models often result in a situation where computing the likelihood of observed data is intractable, while simulating from the conditional density given a parameter value is relatively easy. Approximate Bayesian…
This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a method for rapidly computing the evidence and parameters of probabilistic models that differ only in…
It has been conjectured that the sequence $(3/2)^n$ modulo $1$ is uniformly distributed. The distribution of this sequence is signifcant in relation to unsolved problems in number theory including the Collatz conjecture. In this paper, we…
Selecting between different dependency structures of hidden Markov random field can be very challenging, due to the intractable normalizing constant in the likelihood. We answer this question with approximate Bayesian computation (ABC)…
In many statistical problems, a more coarse-grained model may be suitable for population-level behaviour, whereas a more detailed model is appropriate for accurate modelling of individual behaviour. This raises the question of how to…
Supervised topic models with a logistic likelihood have two issues that potentially limit their practical use: 1) response variables are usually over-weighted by document word counts; and 2) existing variational inference methods make…
Blocking, a special case of rerandomization, is routinely implemented in the design stage of randomized experiments to balance the baseline covariates. This study proposes a regression adjustment method based on the least absolute shrinkage…
We develop a novel method for carrying out model selection for Bayesian autoencoders (BAEs) by means of prior hyper-parameter optimization. Inspired by the common practice of type-II maximum likelihood optimization and its equivalence to…