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Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of…
We present quantum algorithms for sampling from non-logconcave probability distributions in the form of $\pi(x) \propto \exp(-\beta f(x))$. Here, $f$ can be written as a finite sum $f(x):= \frac{1}{N}\sum_{k=1}^N f_k(x)$. Our approach is…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
The authors present a new molecular dynamics algorithm for sampling the isothermal-isobaric ensemble. In this approach the velocities of all particles and volume degrees of freedom are rescaled by a properly chosen random factor. The…
Stochastic approximation (SA) algorithms are widely used in system optimization problems when only noisy measurements of the system are available. This paper studies two types of SA algorithms in a multivariate Kiefer-Wolfowitz setting:…
Most existing approximate Thompson Sampling (TS) algorithms for multi-armed bandits use Stochastic Gradient Langevin Dynamics (SGLD) or its variants in each round to sample from the posterior, relaxing the need for conjugacy assumptions…
Stochastic gradient Langevin dynamics and its variants approximate the likelihood of an entire dataset, via random (and typically much smaller) subsets, in the setting of Bayesian sampling. Due to the (often substantial) improvement of the…
Optimal experimental design (OED) seeks experiments expected to yield the most useful data for some purpose. In practical circumstances where experiments are time-consuming or resource-intensive, OED can yield enormous savings. We pursue…
Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…
Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…
We propose a system identification method, Non-Markovian Optimization-based Modeling for Approximate Dynamics with Spatially-homogeneous memory (NOMADS), for identifying linear dynamical systems from a set of multi-dimensional time-series…
Machine learning-based simulators offer the potential to model the dynamics of complex systems more efficiently than classical approaches, while retaining differentiability, a key property for materials design. Graph neural network…
Stochastic gradient methods (SGMs) are predominant approaches for solving stochastic optimization. On smooth nonconvex problems, a few acceleration techniques have been applied to improve the convergence rate of SGMs. However, little…
We propose the stochastic optimal path which solves the classical optimal path problem by a probability-softening solution. This unified approach transforms a wide range of DP problems into directed acyclic graphs in which all paths follow…
Stochastic variance-reduced algorithms such as Stochastic Average Gradient (SAG) and SAGA, and their deterministic counterparts like the Incremental Aggregated Gradient (IAG) method, have been extensively studied in large-scale machine…
Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, specially when the objective is to improve the performance of a stochastic system. However, the performance of these…
We analyze the complexity of biased stochastic gradient methods (SGD), where individual updates are corrupted by deterministic, i.e. biased error terms. We derive convergence results for smooth (non-convex) functions and give improved rates…
Conformational sampling of biomolecules using molecular dynamics simulations often produces large amount of high dimensional data that makes it difficult to interpret using conventional analysis techniques. Dimensionality reduction methods…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
The Gibbs sampler (GS) is a crucial algorithm for approximating complex calculations, and it is justified by Markov chain theory, the alternating projection theorem, and $I$-projection, separately. We explore the equivalence between these…