Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian regularizations in a specific category of DNNs, i.e., Convolutional Neural Networks (CNNs). First, we introduce a novel probabilistic representation for the hidden layers of CNNs and demonstrate that CNNs correspond to Bayesian networks with the serial connection. Furthermore, we show that the hidden layers close to the input formulate prior distributions, thus CNNs have explicitly Bayesian regularizations based on the Bayesian regularization theory. In addition, we clarify two recently observed empirical phenomena that are inconsistent with traditional theories of generalization. Finally, we validate the proposed theory on a synthetic dataset

Deductive formalisms have been strongly developed in recent years; among them, Answer Set Programming (ASP) gained some momentum, and has been lately fruitfully employed in many real-world scenarios. Nonetheless, in spite of a large number of success stories in relevant application areas, and even in industrial contexts, deductive reasoning cannot be considered the ultimate, comprehensive solution to AI; indeed, in several contexts, other approaches result to be more useful. Typical Bioinformatics tasks, for instance classification, are currently carried out mostly by Machine Learning (ML) based solutions. In this paper, we focus on the relatively new problem of analyzing the evolution of neurological disorders. In this context, ML approaches already demonstrated to be a viable solution for classification tasks; here, we show how ASP can play a relevant role in the brain evolution simulation task. In particular, we propose a general and extensible framework to support physicians and researchers at understanding the complex mechanisms underlying neurological disorders. The framework relies on a combined use of ML and ASP, and is general enough to be applied in several other application scenarios, which are outlined in the paper.

Metric learning for classification has been intensively studied over the last decade. The idea is to learn a metric space induced from a normed vector space on which data from different classes are well separated. Different measures of the separation thus lead to various designs of the objective function in the metric learning model. One classical metric is the Mahalanobis distance, where a linear transformation matrix is designed and applied on the original dataset to obtain a new subspace equipped with the Euclidean norm. The kernelized version has also been developed, followed by Multiple-Kernel learning models. In this paper, we consider metric learning to be the identification of the best kernel function with respect to a high class separability in the corresponding metric space. The contribution is twofold: 1) No pairwise computations are required as in most metric learning techniques; 2) Better flexibility and lower computational complexity is achieved using the CLAss-Specific (Multiple) Kernel - Metric Learning (CLAS(M)K-ML). The proposed techniques can be considered as a preprocessing step to any kernel method or kernel approximation technique. An extension to a hierarchical learning structure is also proposed to further improve the classification performance, where on each layer, the CLASMK is computed based on a selected "marginal" subset and feature vectors are constructed by concatenating the features from all previous layers.

Since then, they have received continuously growing attention. ResNets have a recursive structure x k 1 x k R k( x k) where R k is a neural network and the copying of the input x k is called a skip connection. This structure can be seen as the explicit Euler discretisation of an associated ordinary differential equation (ODE) and this inspired intensive research. However, all of those works only consider the connection of ResNets to a relatively small class of ODEs. We show that by simultaneously increasing the number of skip connection as well as the expressivity of the networks R k the flow for an arbitrary right hand side f L 1 null I; C 0, 1 b (R d; R d)null can be approximated uniformly by deep ReLU ResNets on compact sets. Further, we derive estimates on the number of parameters needed to do this up to a prescribed accuracy under temporal regularity assumptions. We also give a self-contained introduction to the preliminaries regarding neural networks and differential equations. Here, we give an elementary proof for a quantitative universal approximation theorem for deep ReLU networks and see that weak ODEs with right hand side in L 1null I; C 0, 1 b (R d; R d)null are globally well posed. Finally, we discuss the possibility of using ResNets for diffeomorphic matching problems and propose some next steps in the theoretical foundation of this approach.

Abstract: We propose a joint simulation and real-world learning framework for mapping navigation instructions and raw first-person observations to continuous control. Our model estimates the need for environment exploration, predicts the likelihood of visiting environment positions during execution, and controls the agent to both explore and visit high-likelihood positions. We introduce Supervised Reinforcement Asynchronous Learning (SuReAL). Learning uses both simulation and real environments without requiring autonomous flight in the physical environment during training, and combines supervised learning for predicting positions to visit and reinforcement learning for continuous control. We evaluate our approach on a natural language instruction-following task with a physical quad-copter, and demonstrate effective execution and exploration behavior.

We present an adaptive imaging technique that optically computes a low-rank approximation of a scene's hyperspectral image, conceptualized as a matrix. Central to the proposed technique is the optical implementation of two measurement operators: a spectrally-coded imager and a spatially-coded spectrometer. By iterating between the two operators, we show that the top singular vectors and singular values of a hyperspectral image can be adaptively and optically computed with only a few iterations. We present an optical design that uses pupil plane coding for implementing the two operations and show several compelling results using a lab prototype to demonstrate the effectiveness of the proposed hyperspectral imager.

The estimation of f τ( x) is difficult but, more informative than estimation of only mean regression f ( x). The estimation of f τ( x) for different values of τ can briefly describe the different characteristics of the conditional distribution of y/x . In many real world problems, the estimation of mean regression f ( x) is not required or enough, rather they require the estimation of quantile f τ(x). The study of quantile regression problem has initially been started in 1978 by Koenkar and Bassett[1]. Later, it has been briefly discussed and described by Koenker in his book (Koenker, [2]). Koenkar and Bassett [1] proposed the pinball loss function for the estimation of the quantile function f τ(x). For a given quantile τ (0, 1), the pinball loss function was an asymmetric loss function suitable for quantile estimation. It was given by P τ( u) null τu if u 0, (τ 1)u otherwise.

Collaborative filtering has witnessed significant improvem ents in recent years, largely due to models based on low-dimensional embeddings, like weighted matrix factorizati on (e.g., [26, 39]) and deep learning [23, 22, 33, 47, 62, 58, 20, 11], including autoencoders [58, 33]. Also neighborhoo d-based approaches are competitive in certain regimes (e.g., [1, 53, 54]), despite being simple heuristics based o n item-item (or user-user) similarity matrices (like cosin e similarity). In this paper, we outline that Markov Random Fi elds (MRF) are closely related to autoencoders as well as to neighborhood-based approaches. W e build on the enormo us progress made in learning MRFs, in particular in sparse inverse covariance estimation (e.g., [36, 59, 15, 2, 60, 44, 45, 63, 55, 24, 25, 52, 56, 51]). Much of the literature on sparse inverse covariance estimation focuses on the regi me where the number of data points n is much smaller than the number of variables m in the model ( n m).

To overcome the absence of training data for unseen classes, conventional zero-shot learning approaches mainly train their model on seen datapoints and leverage the semantic descriptions for both seen and unseen classes. Beyond exploiting relations between classes of seen and unseen, we present a deep generative model to provide the model with experience about both seen and unseen classes. Based on the variational auto-encoder with class-specific multi-modal prior, the proposed method learns the conditional distribution of seen and unseen classes. In order to circumvent the need for samples of unseen classes, we treat the non-existing data as missing examples. That is, our network aims to find optimal unseen datapoints and model parameters, by iteratively following the generating and learning strategy. Since we obtain the conditional generative model for both seen and unseen classes, classification as well as generation can be performed directly without any off-the-shell classifiers. In experimental results, we demonstrate that the proposed generating and learning strategy makes the model achieve the outperforming results compared to that trained only on the seen classes, and also to the several state-of-the-art methods.

JOURNAL OF L A T EX CLASS FILES, VOL., NO., 1 Single V ersus Union: Nonparallel Support V ector Machine Frameworks Chun-Na Li, Y uan-Hai Shao, Huajun Wang, Y u-Ting Zhao, Ling-Wei Huang, Naihua Xiu and Nai-Y ang Deng Abstract --Considering the classification problem, we summarize the nonparallel support vector machines with the nonparallel hyperplanes to two types of frameworks. It solves a series of small optimization problems to obtain a series of hyperplanes, but is hard to measure the loss of each sample. The other type constructs all the hyperplanes simultaneously, and it solves one big optimization problem with the ascertained loss of each sample. We give the characteristics of each framework and compare them carefully. In addition, based on the second framework, we construct a max-min distance-based nonparallel support vector machine for multiclass classification problem, called NSVM. Experimental results on benchmark data sets and human face databases show the advantages of our NSVM. I NTRODUCTION F OR binary classification problem, the generalized eigenvalue proximal support vector machine (GEPSVM) was proposed by Mangasarian and Wild [1] in 2006, which is the first nonparallel support vector machine. It aims at generating two nonparallel hyperplanes such that each hyperplane is closer to its class and as far as possible from the other class. GEPSVM is effective, particularly when dealing with the "Xor"-type data [1]. This leads to extensive studies on nonparallel support vector machines (NSVMs) [2]-[5].