Related papers: Approximate is Good Enough: Probabilistic Variants…
Modern deep learning methods provide effective means to learn good representations. However, is a good representation itself sufficient for sample efficient reinforcement learning? This question has largely been studied only with respect to…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general…
The aim of this note is to construct a neural network for which the linear finite element approximation of a simple one dimensional boundary value problem is a minimum of the cost function to find out if the neural network is able to…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
Large margin nearest neighbor (LMNN) is a metric learner which optimizes the performance of the popular $k$NN classifier. However, its resulting metric relies on pre-selected target neighbors. In this paper, we address the feasibility of…
Although recent provable methods have been developed to compute preimage bounds for neural networks, their scalability is fundamentally limited by the #P-hardness of the problem. In this work, we adopt a novel probabilistic perspective,…
We define a special network that exhibits the large embeddings in any class of similar algebras. With the aid of this network, we introduce a notion of distance that conceivably counts the minimum number of dissimilarities, in a sense,…
Despite their many appealing properties, kernel methods are heavily affected by the curse of dimensionality. For instance, in the case of inner product kernels in $\mathbb{R}^d$, the Reproducing Kernel Hilbert Space (RKHS) norm is often…
Knowledge compilation studies the trade-off between succinctness and efficiency of different representation languages. For many languages, there are known strong lower bounds on the representation size, but recent work shows that, for some…
Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…
Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We consider functions defined by deep neural networks as definable objects in an o-miminal expansion of the real field, and derive an almost linear (in the number of weights) bound on sample complexity of such networks.
We study the approximation capabilities of two families of univariate polynomials that arise in applications of quantum signal processing. Although approximation only in the domain $[0,1]$ is physically desired, these polynomial families…
Conditional density estimation is a general framework for solving various problems in machine learning. Among existing methods, non-parametric and/or kernel-based methods are often difficult to use on large datasets, while methods based on…
In this paper, we propose a novel image set representation and classification method by maximizing the margin of image sets. The margin of an image set is defined as the difference of the distance to its nearest image set from different…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two…