Related papers: Convergence of the Expectation-Maximization Algori…
The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of…
This paper studies economic model predictive Control (EMPC) schemes, where the stage cost depends only on control inputs. Such problems arise in applications like water distribution networks and differ from standard EMPC since multiple…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
Pel-recursive motion estimation isa well-established approach. However, in the presence of noise, it becomes an ill-posed problem that requires regularization. In this paper, motion vectors are estimated in an iterative fashion by means of…
We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts: a treatment of these algorithms at the population level (in…
Optimization plays a central role in intelligent systems and cyber-physical technologies, where speed and reliability of convergence directly impact performance. In control theory, optimization-centric methods are standard: controllers are…
Recently, there has been an increasing interest in using tools from dynamical systems to analyze the behavior of simple optimization algorithms such as gradient descent and accelerated variants. This paper strengthens such connections by…
We study the expectation-maximization (EM) algorithm for general latent-variable models under (i) distributional misspecification and (ii) nonidentifiability induced by a group action. We formulate EM on the quotient parameter space and…
In this paper, we firstly give a brief introduction of expectation maximization (EM) algorithm, and then discuss the initial value sensitivity of expectation maximization algorithm. Subsequently, we give a short proof of EM's convergence.…
This paper considers an approximate dynamic matrix factor model that accounts for the time series nature of the data by explicitly modelling the time evolution of the factors. We study estimation of the model parameters based on the…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
In current model-free reinforcement learning (RL) algorithms, stability criteria based on sampling methods are commonly utilized to guide policy optimization. However, these criteria only guarantee the infinite-time convergence of the…
In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…
The Expectation-Maximization (EM) algorithm is a popular choice for learning latent variable models. Variants of the EM have been initially introduced, using incremental updates to scale to large datasets, and using Monte Carlo (MC)…
Jump Markov linear systems (JMLS) are a useful class which can be used to model processes which exhibit random changes in behavior during operation. This paper presents a numerically stable method for learning the parameters of jump Markov…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable open-loop system. The…
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
We show how the expectation-maximization (EM) algorithm can be applied exactly for the fitting of mixtures of general multivariate skew t (MST) distributions, eliminating the need for computationally expensive Monte Carlo estimation. Finite…