相关论文: Learning PSD-valued functions using kernel sums-of…

In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…

Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive…

Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional…

In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding…

We associate to a real projective variety $X$ two convex cones which are fundamental in real algebraic geometry: the cone $P_X$ of quadratic forms nonnegative on $X$, and the cone $\Sigma_X$ of sums of squares of linear forms. The dual cone…

We propose a computationally tractable method for the identification of stable canonical discrete-time rational transfer function models, using frequency domain data. The problem is formulated as a global non-convex optimization problem…

The paper introduces the weighted convolution, a novel approach to the convolution for signals defined on regular grids (e.g., 2D images) through the application of an optimal density function to scale the contribution of neighbouring…

Recently, various convolutions based on continuous or discrete kernels for point cloud processing have been widely studied, and achieve impressive performance in many applications, such as shape classification, scene segmentation and so on.…

We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…

Accurate and efficient environment representation is crucial for robotic applications such as motion planning, manipulation, and navigation. Signed distance functions (SDFs) have emerged as a powerful representation for encoding distance to…

We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision…

State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…

Machine learning for differential equations paves the way for computationally efficient alternatives to numerical solvers, with potentially broad impacts in science and engineering. Though current algorithms typically require simulated…

Let $x_1,x_2,\ldots,x_m$ be elements of a convex cone $K$ such that their sum, $e$, is in the relative interior of $K$. An $\epsilon$-sparsification of the sum involves taking a subset of the $x_i$ and reweighting them by positive scalars,…

Non-convex optimization problems are ubiquitous in machine learning, especially in Deep Learning. While such complex problems can often be successfully optimized in practice by using stochastic gradient descent (SGD), theoretical analysis…

Sum of squares (SOS) optimization is a powerful technique for solving problems where the positivity of a polynomials must be enforced. The common approach to solve an SOS problem is by relaxation to a Semidefinite Program (SDP). The main…

We investigate the problem of finding inner ap-proximations of positive semidefinite (PSD) cones. We developa novel decomposition framework of the PSD cone by meansof conical combinations of smaller dimensional sub-cones. Weshow that many…

Differential geometric approaches to the analysis and processing of data in the form of symmetric positive definite (SPD) matrices have had notable successful applications to numerous fields including computer vision, medical imaging, and…

We propose a kernel-based nonparametric framework for mean-variance optimization that enables inference on economically motivated shape constraints in finance, including positivity, monotonicity, and convexity. Many central hypotheses in…

This paper examines the application of the Kernel Sum of Squares (KSOS) method for enhancing kernel learning from data, particularly in the context of dynamical systems. Traditional kernel-based methods, despite their theoretical soundness…