Related papers: A Variational Principle Based Study of KPP Minimal…
We consider the fundamental problem of learning the parameters of an undirected graphical model or Markov Random Field (MRF) in the setting where the edge weights are chosen at random. For Ising models, we show that a multiplicative-weight…
Probabilistic shaping (PS) is investigated as a potential technique to approach the Shannon limit. However, it has been proved that conventional carrier phase recovery (CPR) algorithm designed for uniform distribution may have extra penalty…
Stochastic gradient descent (SGD) is a cornerstone of machine learning. When the number N of data items is large, SGD relies on constructing an unbiased estimator of the gradient of the empirical risk using a small subset of the original…
While nowadays most gradient-based optimization methods focus on exploring the high-dimensional geometric features, the random error accumulated in a stochastic version of any algorithm implementation has not been stressed yet. In this…
We study average-reward Markov decision processes (AMDPs) and develop novel first-order methods with strong theoretical guarantees for both policy optimization and policy evaluation. Compared with intensive research efforts in finite sample…
Piecewise deterministic Markov processes (PDMPs) are a class of continuous-time Markov processes that were recently used to develop a new class of Markov chain Monte Carlo algorithms. However, the implementation of the processes is…
Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…
A piecewise-deterministic Markov process is a stochastic process whose behavior is governed by an ordinary differential equation punctuated by random jumps occurring at random times. We focus on the nonparametric estimation problem of the…
It is well known that the fluid-particle acceleration is intimately related to the dissipation rate of turbulence, in line with the Kolmogorov assumptions. On the other hand, various experimental and numerical works have reported as well…
Analysing stationary point databases to extract phenomenological rate constants can become time-consuming for systems with large potential energy barriers. In the present contribution we analyse several different approaches to this problem.…
Markov jump processes (MJPs) are used to model a wide range of phenomena from disease progression to RNA path folding. However, maximum likelihood estimation of parametric models leads to degenerate trajectories and inferential performance…
A probabilistic machine learning model is introduced to augment the $k-\omega\ SST$ turbulence model in order to improve the modelling of separated flows and the generalisability of learnt corrections. Increasingly, machine learning methods…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…
This paper investigates the existence of almost periodic traveling fronts for Fisher-KPP lattice equations in one-dimensional almost periodic media. By the Lyapunov exponent of the linearized operator near the unstable steady state, we give…
The stable principal component pursuit (SPCP) is a non-smooth convex optimization problem, the solution of which enables one to reliably recover the low rank and sparse components of a data matrix which is corrupted by a dense noise matrix,…
We study variational principles for metric mean dimension. First we prove that in the variational principle of Lindenstrauss and Tsukamoto it suffices to take supremum over ergodic measures. Second we derive a variational principle for…
Randomized-subspace methods reduce the cost of first-order optimization by using only low-dimensional projected-gradient information, a feature that is attractive in forward-mode automatic differentiation and communication-limited settings.…
Determinantal Point Processes (DPPs) are elegant probabilistic models of repulsion and diversity over discrete sets of items. But their applicability to large sets is hindered by expensive cubic-complexity matrix operations for basic tasks…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…