Selecting hyperparameters for unsupervised learning problems is difficult in general due to the lack of ground truth for validation. However, this issue is prevalent in machine learning, especially in clustering problems with examples including the Lagrange multipliers of penalty terms in semidefinite programming (SDP) relaxations and the bandwidths used for constructing kernel similarity matrices for Spectral Clustering. Despite this, there are not many provable algorithms for tuning these hyperparameters. In this paper, we provide a unified framework with provable guarantees for the above class of problems. We demonstrate our method on two distinct models.

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.

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.

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].

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often refereed to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of hitherto attempts at handling uncertainty in general and formalizing this distinction in particular. 1 Introduction Machine learning is essentially concerned with extracting models from data and using these models to make predictions.

In this work, we develop a novel framework to measure the similarity between dynamic financial networks, i.e., time-varying financial networks. Particularly, we explore whether the proposed similarity measure can be employed to understand the structural evolution of the financial networks with time. For a set of time-varying financial networks with each vertex representing the individual time series of a different stock and each edge between a pair of time series representing the absolute value of their Pearson correlation, our start point is to compute the commute time matrix associated with the weighted adjacency matrix of the network structures, where each element of the matrix can be seen as the enhanced correlation value between pairwise stocks. For each network, we show how the commute time matrix allows us to identify a reliable set of dominant correlated time series as well as an associated dominant probability distribution of the stock belonging to this set. Furthermore, we represent each original network as a discrete dominant Shannon entropy time series computed from the dominant probability distribution. With the dominant entropy time series for each pair of financial networks to hand, we develop a similarity measure based on the classical dynamic time warping framework, for analyzing the financial time-varying networks. We show that the proposed similarity measure is positive definite and thus corresponds to a kernel measure on graphs. The proposed kernel bridges the gap between graph kernels and the classical dynamic time warping framework for multiple financial time series analysis. Experiments on time-varying networks extracted through New York Stock Exchange (NYSE) database demonstrate the effectiveness of the proposed approach.