Related papers: Dp-rank and forbidden configurations
We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems. DPC poses an approximate solution to multiparametric programming problems emerging from explicit nonlinear…
We present a novel analysis of the dynamics of tensor power iterations in the overcomplete regime where the tensor CP rank is larger than the input dimension. Finding the CP decomposition of an overcomplete tensor is NP-hard in general. We…
While MPC enables nonlinear feedback control by solving an optimal control problem at each timestep, the computational burden tends to be significantly large, making it difficult to optimize a policy within the control period. To address…
We introduce the matrix-based Renyi's $\alpha$-order entropy functional to parameterize Tishby et al. information bottleneck (IB) principle with a neural network. We term our methodology Deep Deterministic Information Bottleneck (DIB), as…
Two inertial DC algorithms for indefinite quadratic programs under linear constraints (IQPs) are considered in this paper. Using a qualification condition related to the normal cones of unbounded pseudo-faces of the polyhedral convex…
We propose a novel approach to solving input- and state-constrained parametric mixed-integer optimal control problems using Differentiable Predictive Control (DPC). Our approach follows the differentiable programming paradigm by learning an…
This chapter provides a comprehensive and self-contained discussion of the most recent developments of information theory of networks. Maximum entropy models of networks are the least biased ensembles enforcing a set of constraints and are…
Randomized controlled trials typically analyze the effectiveness of treatments with the goal of making treatment recommendations for patient subgroups. With the advance of electronic health records, a great variety of data has been…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
In this short note we prove an estimate on the rank a.e. of the tangent (p,p) vector to a a positive closed current of bidimension (p,p) in CP^k, in terms of the dimension of its trace measure.
We give several characterizations of when a complete first-order theory $T$ is monadically NIP, i.e. when expansions of $T$ by arbitrary unary predicates do not have the independence property. The central characterization is a condition on…
Traditionally a tiling is defined with a finite number of finite forbidden patterns. We can generalize this notion considering any set of patterns. Generalized tilings defined in this way can be studied with a dynamical point of view,…
Opacity, or non-interference, is a property ensuring that an external observer cannot infer confidential information (the "secret") from system observations. We introduce an information-theoretic measure of opacity, which quantifies…
World models enable long-horizon planning by internally generating and evaluating imagined trajectories, making them a promising foundation for generalist agents. However, this imagination-driven decision process also introduces new…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…
We provide a finite forbidden induced subgraph characterization for the graph class $\varUpsilon_k$, for all $k \in \mathbb{N}_0$, which is defined as follows. A graph is in $\varUpsilon_k$ if for any induced subgraph, $\Delta \leq \chi -1…
Tensor Network (TN) decompositions have emerged as an indispensable tool in Big Data analytics owing to their ability to provide compact low-rank representations, thus alleviating the ``Curse of Dimensionality'' inherent in handling…
We introduce the following variant of the VC-dimension. Given $S \subseteq \{0, 1\}^n$ and a positive integer $d$, we define $\mathbb{U}_d(S)$ to be the size of the largest subset $I \subseteq [n]$ such that the projection of $S$ on every…
This paper shows how maximum possible configuration efficiency of an indefinitely large software system is constrained by chosing a fixed upper limit to the number of program units per subsystem. It is then shown how the configuration…
The goal of this manuscript is to conduct a controltheoretic analysis of Temporal Difference (TD) learning algorithms. TD-learning serves as a cornerstone in the realm of reinforcement learning, offering a methodology for approximating the…