Classification with Costly Features using Deep Reinforcement Learning

We study a classification problem where each feature can be acquired for a cost and the goal is to optimize a trade-off between the expected classification error and the feature cost. We revisit a former approach that has framed the problem as a sequential decision-making problem and solved it by Q-learning with a linear approximation, where individual actions are either requests for feature values or terminate the episode by providing a classification decision. On a set of eight problems, we demonstrate that by replacing the linear approximation with neural networks the approach becomes comparable to the state-of-the-art algorithms developed specifically for this problem. The approach is flexible, as it can be improved with any new reinforcement learning enhancement, it allows inclusion of pre-trained high-performance classifier, and unlike prior art, its performance is robust across all evaluated datasets.Comment: AAAI 201

Beating the Perils of Non-Convexity: Guaranteed Training of Neural Networks using Tensor Methods

Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of two-layer neural networks. We provide risk bounds for our proposed method, with a polynomial sample complexity in the relevant parameters, such as input dimension and number of neurons. While learning arbitrary target functions is NP-hard, we provide transparent conditions on the function and the input for learnability. Our training method is based on tensor decomposition, which provably converges to the global optimum, under a set of mild non-degeneracy conditions. It consists of simple embarrassingly parallel linear and multi-linear operations, and is competitive with standard stochastic gradient descent (SGD), in terms of computational complexity. Thus, we propose a computationally efficient method with guaranteed risk bounds for training neural networks with one hidden layer.Comment: The tensor decomposition analysis is expanded, and the analysis of ridge regression is added for recovering the parameters of last layer of neural networ

Distribution-Based Categorization of Classifier Transfer Learning

Transfer Learning (TL) aims to transfer knowledge acquired in one problem, the source problem, onto another problem, the target problem, dispensing with the bottom-up construction of the target model. Due to its relevance, TL has gained significant interest in the Machine Learning community since it paves the way to devise intelligent learning models that can easily be tailored to many different applications. As it is natural in a fast evolving area, a wide variety of TL methods, settings and nomenclature have been proposed so far. However, a wide range of works have been reporting different names for the same concepts. This concept and terminology mixture contribute however to obscure the TL field, hindering its proper consideration. In this paper we present a review of the literature on the majority of classification TL methods, and also a distribution-based categorization of TL with a common nomenclature suitable to classification problems. Under this perspective three main TL categories are presented, discussed and illustrated with examples

Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network

Because of their effectiveness in broad practical applications, LSTM networks have received a wealth of coverage in scientific journals, technical blogs, and implementation guides. However, in most articles, the inference formulas for the LSTM network and its parent, RNN, are stated axiomatically, while the training formulas are omitted altogether. In addition, the technique of "unrolling" an RNN is routinely presented without justification throughout the literature. The goal of this paper is to explain the essential RNN and LSTM fundamentals in a single document. Drawing from concepts in signal processing, we formally derive the canonical RNN formulation from differential equations. We then propose and prove a precise statement, which yields the RNN unrolling technique. We also review the difficulties with training the standard RNN and address them by transforming the RNN into the "Vanilla LSTM" network through a series of logical arguments. We provide all equations pertaining to the LSTM system together with detailed descriptions of its constituent entities. Albeit unconventional, our choice of notation and the method for presenting the LSTM system emphasizes ease of understanding. As part of the analysis, we identify new opportunities to enrich the LSTM system and incorporate these extensions into the Vanilla LSTM network, producing the most general LSTM variant to date. The target reader has already been exposed to RNNs and LSTM networks through numerous available resources and is open to an alternative pedagogical approach. A Machine Learning practitioner seeking guidance for implementing our new augmented LSTM model in software for experimentation and research will find the insights and derivations in this tutorial valuable as well.Comment: 43 pages, 10 figures, 78 reference