ﻻ يوجد ملخص باللغة العربية
Rectified linear units, or ReLUs, have become the preferred activation function for artificial neural networks. In this paper we consider two basic learning problems assuming that the underlying data follow a generative model based on a ReLU-network -- a neural network with ReLU activations. As a primarily theoretical study, we limit ourselves to a single-layer network. The first problem we study corresponds to dictionary-learning in the presence of nonlinearity (modeled by the ReLU functions). Given a set of observation vectors $mathbf{y}^i in mathbb{R}^d, i =1, 2, dots , n$, we aim to recover $dtimes k$ matrix $A$ and the latent vectors ${mathbf{c}^i} subset mathbb{R}^k$ under the model $mathbf{y}^i = mathrm{ReLU}(Amathbf{c}^i +mathbf{b})$, where $mathbf{b}in mathbb{R}^d$ is a random bias. We show that it is possible to recover the column space of $A$ within an error of $O(d)$ (in Frobenius norm) under certain conditions on the probability distribution of $mathbf{b}$. The second problem we consider is that of robust recovery of the signal in the presence of outliers, i.e., large but sparse noise. In this setting we are interested in recovering the latent vector $mathbf{c}$ from its noisy nonlinear sketches of the form $mathbf{v} = mathrm{ReLU}(Amathbf{c}) + mathbf{e}+mathbf{w}$, where $mathbf{e} in mathbb{R}^d$ denotes the outliers with sparsity $s$ and $mathbf{w} in mathbb{R}^d$ denote the dense but small noise. This line of work has recently been studied (Soltanolkotabi, 2017) without the presence of outliers. For this problem, we show that a generalized LASSO algorithm is able to recover the signal $mathbf{c} in mathbb{R}^k$ within an $ell_2$ error of $O(sqrt{frac{(k+s)log d}{d}})$ when $A$ is a random Gaussian matrix.
We address the problem of model selection for the finite horizon episodic Reinforcement Learning (RL) problem where the transition kernel $P^*$ belongs to a family of models $mathcal{P}^*$ with finite metric entropy. In the model selection framework,
Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This motivates us t
In this paper, we propose a new global analysis framework for a class of low-rank matrix recovery problems on the Riemannian manifold. We analyze the global behavior for the Riemannian optimization with random initialization. We use the Riemannian gr
An associative memory is a framework of content-addressable memory that stores a collection of message vectors (or a dataset) over a neural network while enabling a neurally feasible mechanism to recover any message in the dataset from its noisy vers
As artificial intelligence is increasingly affecting all parts of society and life, there is growing recognition that human interpretability of machine learning models is important. It is often argued that accuracy or other similar generalization per