Related papers: Maximum Entropy Vector Kernels for MIMO system ide…
Through one decade's development, the kernel-based regularization method (KRM) has become a complement to the classical maximum likelihood/prediction error method and an emerging new system identification paradigm. One recent example is its…
In this paper we study the kernel multiple ridge regression framework, which we refer to as multi-task regression, using penalization techniques. The theoretical analysis of this problem shows that the key element appearing for an optimal…
Behavioural metrics have been shown to be an effective mechanism for constructing representations in reinforcement learning. We present a novel perspective on behavioural metrics for Markov decision processes via the use of positive…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem…
This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix of a prespecified size from a covariance matrix. MESP has been widely applied to many areas, including…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
Differential privacy has become a cornerstone in the development of privacy-preserving learning algorithms. This work addresses optimizing differentially private kernel learning within the empirical risk minimization (ERM) framework. We…
We review here {\it Maximum Caliber} (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of {\it Maximum Entropy} (Max…
We revisit the classical problem of inverting dimension-reducing linear mappings using the maximum entropy (MaxEnt) criterion. In the literature, solutions are problem-dependent, inconsistent, and use different entropy measures. We propose…
In this paper, we are concerned with estimating the joint probability of random variables $X$ and $Y$, given $N$ independent observation blocks $(\boldsymbol{x}^i,\boldsymbol{y}^i)$, $i=1,\ldots,N$, each of $M$ samples…
Much recent work in bioinformatics has focused on the inference of various types of biological networks, representing gene regulation, metabolic processes, protein-protein interactions, etc. A common setting involves inferring network edges…
We present an algorithm for L1-norm kernel PCA and provide a convergence analysis for it. While an optimal solution of L2-norm kernel PCA can be obtained through matrix decomposition, finding that of L1-norm kernel PCA is not trivial due to…
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…
In this paper, we address the identification problem for the systems characterized by linear time-invariant dynamics with bilinear observation models. More precisely, we consider a suitable parametric description of the system and formulate…
We introduce the $\ell_0\ell_2$-norm regularization and hierarchy constraints into linear regression for the construction of cluster expansion to describe configurational disorder in materials. The approach is implemented through mixed…
Massive MIMO has been regarded as a key enabling technique for 5G and beyond networks. Nevertheless, its performance is limited by the large overhead needed to obtain the high-dimensional channel information. To reduce the huge training…
Maximum Entropy is an image reconstruction method conceived to image a sparsely occupied field of view and therefore particularly appropriate to achieve super-resolution effects. Although widely used in image deconvolution, this method has…
Mixed linear regression involves the recovery of two (or more) unknown vectors from unlabeled linear measurements; that is, where each sample comes from exactly one of the vectors, but we do not know which one. It is a classic problem, and…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…