Related papers: Near-Optimality of Contrastive Divergence Algorith…
The Contrastive Divergence (CD) algorithm has achieved notable success in training energy-based models including Restricted Boltzmann Machines and played a key role in the emergence of deep learning. The idea of this algorithm is to…
In our recent paper, we showed that in exponential family, contrastive divergence (CD) with fixed learning rate will give asymptotically consistent estimates \cite{wu2016convergence}. In this paper, we establish consistency and convergence…
Contrastive divergence (CD) learning is a classical method for fitting unnormalized statistical models to data samples. Despite its wide-spread use, the convergence properties of this algorithm are still not well understood. The main source…
There are many models, often called unnormalized models, whose normalizing constants are not calculated in closed form. Maximum likelihood estimation is not directly applicable to unnormalized models. Score matching, contrastive divergence…
Distributionally robust optimization (DRO) is a widely-used approach to learn models that are robust against distribution shift. Compared with the standard optimization setting, the objective function in DRO is more difficult to optimize,…
Novel coordinate descent (CD) methods are proposed for minimizing nonconvex functions consisting of three terms: (i) a continuously differentiable term, (ii) a simple convex term, and (iii) a concave and continuous term. First, by extending…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
Given a language model (LM), maximum probability is a poor decoding objective for open-ended generation, because it produces short and repetitive text. On the other hand, sampling can often produce incoherent text that drifts from the…
This study reveals the inherent tolerance of contrastive learning (CL) towards sampling bias, wherein negative samples may encompass similar semantics (\eg labels). However, existing theories fall short in providing explanations for this…
We build on recent works on Stein's method for functions of multivariate normal random variables to derive bounds for the rate of convergence of some asymptotically chi-square distributed statistics. We obtain some general bounds and…
Optimal Transport (OT) based distances are powerful tools for machine learning to compare probability measures and manipulate them using OT maps. In this field, a setting of interest is semi-discrete OT, where the source measure $\mu$ is…
This paper proposes $\mathbf{C}$ommunication efficient $\mathbf{RE}$cursive $\mathbf{D}$istributed estimati$\mathbf{O}$n algorithm, $\mathcal{CREDO}$, for networked multi-worker setups without a central master node. $\mathcal{CREDO}$ is…
Contrastive Divergence (CD) and Persistent Contrastive Divergence (PCD) are popular methods for training the weights of Restricted Boltzmann Machines. However, both methods use an approximate method for sampling from the model distribution.…
This paper studies the problem of parameter learning in probabilistic graphical models having latent variables, where the standard approach is the expectation maximization algorithm alternating expectation (E) and maximization (M) steps.…
Energy-based models (EBMs) offer flexible distribution parametrization. However, due to the intractable partition function, they are typically trained via contrastive divergence for maximum likelihood estimation. In this paper, we propose…
Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions,…
We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…
Suppose one has a collection of parameters indexed by a (possibly infinite dimensional) set. Given data generated from some distribution, the objective is to estimate the maximal parameter in this collection evaluated at this distribution.…
Offline reinforcement learning aims to learn from pre-collected datasets without active exploration. This problem faces significant challenges, including limited data availability and distributional shifts. Existing approaches adopt a…
We analyze the convergence rates of two popular variants of coordinate descent (CD): random CD (RCD), in which the coordinates are sampled uniformly at random, and random-permutation CD (RPCD), in which random permutations are used to…