This paper presents Generalized Correspondence-LDA (GC-LDA), a generalization of the Correspondence-LDA model that allows for variable spatial representations to be associated with topics, and increased flexibility in terms of the strength of the correspondence between data types induced by the model. We present three variants of GC-LDA, each of which associates topics with a different spatial representation, and apply them to a corpus of neuroimaging data. In the context of this dataset, each topic corresponds to a functional brain region, where the region's spatial extent is captured by a probability distribution over neural activity, and the region's cognitive function is captured by a probability distribution over linguistic terms. We illustrate the qualitative improvements offered by GC-LDA in terms of the types of topics extracted with alternative spatial representations, as well as the model's ability to incorporate a-priori knowledge from the neuroimaging literature. We furthermore demonstrate that the novel features of GC-LDA improve predictions for missing data.

Recurrent neural networks (RNNs) stand at the forefront of many recent developments in deep learning. Yet a major difficulty with these models is their tendency to overfit, with dropout shown to fail when applied to recurrent layers. Recent results at the intersection of Bayesian modelling and deep learning offer a Bayesian interpretation of common deep learning techniques such as dropout. This grounding of dropout in approximate Bayesian inference suggests an extension of the theoretical results, offering insights into the use of dropout with RNN models. We apply this new variational inference based dropout technique in LSTM and GRU models, assessing it on language modelling and sentiment analysis tasks. The new approach outperforms existing techniques, and to the best of our knowledge improves on the single model state-of-the-art in language modelling with the Penn Treebank (73.4 test perplexity). This extends our arsenal of variational tools in deep learning.

A spectral analysis of the Koopman operator, which is an infinite dimensional linear operator on an observable, gives a (modal) description of the global behavior of a nonlinear dynamical system without any explicit prior knowledge of its governing equations. In this paper, we consider a spectral analysis of the Koopman operator in a reproducing kernel Hilbert space (RKHS). We propose a modal decomposition algorithm to perform the analysis using finite-length data sequences generated from a nonlinear system. The algorithm is in essence reduced to the calculation of a set of orthogonal bases for the Krylov matrix in RKHS and the eigendecomposition of the projection of the Koopman operator onto the subspace spanned by the bases. The algorithm returns a decomposition of the dynamics into a finite number of modes, and thus it can be thought of as a feature extraction procedure for a nonlinear dynamical system. Therefore, we further consider applications in machine learning using extracted features with the presented analysis. We illustrate the method on the applications using synthetic and real-world data.

Active learning enables us to reduce the annotation cost by adaptively selecting unlabeled instances to be labeled. For pool-based active learning, several effective methods with theoretical guarantees have been developed through maximizing some utility function satisfying adaptive submodularity. In contrast, there have been few methods for stream-based active learning based on adaptive submodularity. In this paper, we propose a new class of utility functions, policy-adaptive submodular functions, and prove this class includes many existing adaptive submodular functions appearing in real world problems. We provide a general framework based on policy-adaptive submodularity that makes it possible to convert existing pool-based methods to stream-based methods and give theoretical guarantees on their performance. In addition we empirically demonstrate their effectiveness comparing with existing heuristics on common benchmark datasets.

We present a unified approach for learning the parameters of Sum-Product networks (SPNs). We prove that any complete and decomposable SPN is equivalent to a mixture of trees where each tree corresponds to a product of univariate distributions. Based on the mixture model perspective, we characterize the objective function when learning SPNs based on the maximum likelihood estimation (MLE) principle and show that the optimization problem can be formulated as a signomial program. We construct two parameter learning algorithms for SPNs by using sequential monomial approximations (SMA) and the concave-convex procedure (CCCP), respectively. The two proposed methods naturally admit multiplicative updates, hence effectively avoiding the projection operation. With the help of the unified framework, we also show that, in the case of SPNs, CCCP leads to the same algorithm as Expectation Maximization (EM) despite the fact that they are different in general.

Hybrid methods that utilize both content and rating information are commonly used in many recommender systems. However, most of them use either handcrafted features or the bag-of-words representation as a surrogate for the content information but they are neither effective nor natural enough. To address this problem, we develop a collaborative recurrent autoencoder (CRAE) which is a denoising recurrent autoencoder (DRAE) that models the generation of content sequences in the collaborative filtering (CF) setting. The model generalizes recent advances in recurrent deep learning from i.i.d. input to non-i.i.d. (CF-based) input and provides a new denoising scheme along with a novel learnable pooling scheme for the recurrent autoencoder. To do this, we first develop a hierarchical Bayesian model for the DRAE and then generalize it to the CF setting. The synergy between denoising and CF enables CRAE to make accurate recommendations while learning to fill in the blanks in sequences. Experiments on real-world datasets from different domains (CiteULike and Netflix) show that, by jointly modeling the order-aware generation of sequences for the content information and performing CF for the ratings, CRAE is able to significantly outperform the state of the art on both the recommendation task based on ratings and the sequence generation task based on content information.

Gibbs sampling is a Markov Chain Monte Carlo sampling technique that iteratively samples variables from their conditional distributions. There are two common scan orders for the variables: random scan and systematic scan. Due to the benefits of locality in hardware, systematic scan is commonly used, even though most statistical guarantees are only for random scan. While it has been conjectured that the mixing times of random scan and systematic scan do not differ by more than a logarithmic factor, we show by counterexample that this is not the case, and we prove that that the mixing times do not differ by more than a polynomial factor under mild conditions. To prove these relative bounds, we introduce a method of augmenting the state space to study systematic scan using conductance.

Statistics and Machine Learning Toolbox provides functions and apps to describe, analyze, and model data. You can use descriptive statistics and plots for exploratory data analysis, fit probability distributions to data, generate random numbers for Monte Carlo simulations, and perform hypothesis tests. Regression and classification algorithms let you draw inferences from data and build predictive models. For multidimensional data analysis, Statistics and Machine Learning Toolbox provides feature selection, stepwise regression, principal component analysis (PCA), regularization, and other dimensionality reduction methods that let you identify variables or features that impact your model. The toolbox provides supervised and unsupervised machine learning algorithms, including support vector machines (SVMs), boosted and bagged decision trees, k-nearest neighbor, k-means, k-medoids, hierarchical clustering, Gaussian mixture models, and hidden Markov models.

A plethora of networks is being collected in a growing number of fields, including disease transmission, international relations, social interactions, and others. As data streams continue to grow, the complexity associated with these highly multidimensional connectivity data presents novel challenges. In this paper, we focus on the time-varying interconnections among a set of actors in multiple contexts, called layers. Current literature lacks flexible statistical models for dynamic multilayer networks, which can enhance quality in inference and prediction by efficiently borrowing information within each network, across time, and between layers. Motivated by this gap, we develop a Bayesian nonparametric model leveraging latent space representations. Our formulation characterizes the edge probabilities as a function of shared and layer-specific actors positions in a latent space, with these positions changing in time via Gaussian processes. This representation facilitates dimensionality reduction and incorporates different sources of information in the observed data. In addition, we obtain tractable procedures for posterior computation, inference, and prediction. We provide theoretical results on the flexibility of our model. Our methods are tested on simulations and infection studies monitoring dynamic face-to-face contacts among individuals in multiple days, where we perform better than current methods in inference and prediction.

Machine Learning is a vast area of Computer Science that is concerned with designing algorithms which form good models of the world around us (the data coming from the world around us). Within Machine Learning many tasks are - or can be reformulated as - classification tasks. In classification tasks we are trying to produce a model which can give the correlation between the input data and the class each input belongs to. This model is formed with the feature-values of the input-data. For example, the dataset contains datapoints belonging to the classes Apples, Pears and Oranges and based on the features of the datapoints (weight, color, size etc) we are trying to predict the class. We need some amount of training data to train the Classifier, i.e. form a correct model of the data.