Related papers: Probabilistic Predictability of Stochastic Dynamic…
We give a deterministic, nearly logarithmic-space algorithm that given an undirected graph $G$, a positive integer $r$, and a set $S$ of vertices, approximates the conductance of $S$ in the $r$-step random walk on $G$ to within a factor of…
This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use…
It is shown that under standard hypotheses, if stochastic approximation iterates remain tight, they converge with probability one to what their o.d.e. limit suggests. A simple test for tightness (and therefore a.s. convergence) is provided.…
This paper theoretically reanalyzes the convergence of the mini-batch stochastic gradient descent (SGD) for a structured minimization problem involving a finite-sum function with its gradient being stochastically approximated, and an…
Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…
There are several scoring rules that one can choose from in order to score probabilistic forecasting models or estimate model parameters. Whilst it is generally agreed that proper scoring rules are preferable, there is no clear criterion…
Many machine learning applications and tasks rely on the stochastic gradient descent (SGD) algorithm and its variants. Effective step length selection is crucial for the success of these algorithms, which has motivated the development of…
The performance of model-based control techniques strongly depends on the quality of the employed dynamics model. If strong guarantees are desired, it is therefore common to robustly treat all possible sources of uncertainty, such as model…
Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…
In Score based Generative Modeling (SGMs), the state-of-the-art in generative modeling, stochastic reverse processes are known to perform better than their deterministic counterparts. This paper delves into the heart of this phenomenon,…
Researchers rely on the distance function to model multiple product production using multiple inputs. A stochastic directional distance function (SDDF) allows for noise in potentially all input and output variables. Yet, when estimated, the…
In this paper, we present a novel stochastic output-feedback MPC scheme for distributed systems with additive process and measurement noise. The chance constraints are treated with the concept of probabilistic reachable sets, which, under…
This paper poses a theoretical characterization of the stochastic reachability problem in terms of probability measures, capturing the probability measure of the state of the system that satisfies the reachability specification for all…
We present the numerical estimation of noise parameter induced in the dynamics of the variables by random particle interactions involved in the stochastic chemical oscillator and use it as order parameter to detect the transition from…
Program sensitivity, also known as Lipschitz continuity, describes how small changes in a program's input lead to bounded changes in the output. We propose an average notion of program sensitivity for probabilistic programs---expected…
Trajectory prediction is a fundamental and challenging task for numerous applications, such as autonomous driving and intelligent robots. Currently, most of existing work treat the pedestrian trajectory as a series of fixed two-dimensional…
The classical paradigm of scoring rules is to discriminate between two different forecasts by comparing them with observations. The probability distribution of the observed record is assumed to be perfect as a verification benchmark. In…
The metric properties of the set in which random variables take their values lead to relevant probabilistic concepts. For example, the mean of a random variable is a best predictor in that it minimizes the standard Euclidean distance or…
The probability distributions, as well as the mean values of stochastic currents and fluxes, associated with a driven Langevin process, provide a good and topologically protected measure of how far a stochastic system is driven out of…
Multistage stochastic programming deals with operational and planning problems that involve a sequence of decisions over time while responding to realizations that are uncertain. Algorithms designed to address multistage stochastic linear…