In this paper, we develop a parameter estimation method for factorially parametrized models such as Factorial Gaussian Mixture Model and Factorial Hidden Markov Model. Our contributions are two-fold. First, we show that the emission matrix of the standard Factorial Model is unidentifiable even if the true assignment matrix is known. Secondly, we address the issue of identifiability by making a one component sharing assumption and derive a parameter learning algorithm for this case. Our approach is based on a dictionary learning problem of the form $X = O R$, where the goal is to learn the dictionary $O$ given the data matrix $X$. We argue that due to the specific structure of the activation matrix $R$ in the shared component factorial mixture model, and an incoherence assumption on the shared component, it is possible to extract the columns of the $O$ matrix without the need for alternating between the estimation of $O$ and $R$.

We consider the energy minimization problem for undirected graphical models, also known as MAP-inference problem for Markov random fields which is NP-hard in general. We propose a novel polynomial time algorithm to obtain a part of its optimal non-relaxed integral solution. Our algorithm is initialized with variables taking integral values in the solution of a convex relaxation of the MAP-inference problem and iteratively prunes those, which do not satisfy our criterion for partial optimality. We show that our pruning strategy is in a certain sense theoretically optimal. Also empirically our method outperforms previous approaches in terms of the number of persistently labelled variables. The method is very general, as it is applicable to models with arbitrary factors of an arbitrary order and can employ any solver for the considered relaxed problem. Our method's runtime is determined by the runtime of the convex relaxation solver for the MAP-inference problem.

In the era of deep learning several unsupervised models have been developed to capture the key features in unlabeled handwritten data. Popular among them is the Restricted Boltzmann Machines RBM. However, due to the novelty in handwritten multidialect data, the RBM may fail to generate an efficient representation. In this paper we propose a generative model, the Mode Synthesizing Machine MSM for on-line representation of real life handwritten multidialect language data. The MSM takes advantage of the hierarchical representation of the modes of a data distribution using a two-point error update to learn a sequence of representative multidialects in a generative way. Experiments were performed to evaluate the performance of the MSM over the RBM with the former attaining much lower error values than the latter on both independent and mixed data set.

In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy algorithms, we introduce a deep learning framework that supports both linear and mildly nonlinear measurements, that learns a structured representation from training data, and that efficiently computes a signal estimate. In particular, we apply a stacked denoising autoencoder (SDA), as an unsupervised feature learner. SDA enables us to capture statistical dependencies between the different elements of certain signals and improve signal recovery performance as compared to the CS approach.

Most existing word embedding methods can be categorized into Neural Embedding Models and Matrix Factorization (MF)-based methods. However some models are opaque to probabilistic interpretation, and MF-based methods, typically solved using Singular Value Decomposition (SVD), may incur loss of corpus information. In addition, it is desirable to incorporate global latent factors, such as topics, sentiments or writing styles, into the word embedding model. Since generative models provide a principled way to incorporate latent factors, we propose a generative word embedding model, which is easy to interpret, and can serve as a basis of more sophisticated latent factor models. The model inference reduces to a low rank weighted positive semidefinite approximation problem. Its optimization is approached by eigendecomposition on a submatrix, followed by online blockwise regression, which is scalable and avoids the information loss in SVD. In experiments on 7 common benchmark datasets, our vectors are competitive to word2vec, and better than other MF-based methods.

It has recently been found that Bell scenarios are only a small subclass of interesting setups for studying the non-classical features of quantum theory within spacetime. We find that it is possible to talk about classical correlations, quantum correlations and other kinds of correlations on any directed acyclic graph, and this captures various extensions of Bell scenarios which have been considered in the literature. From a conceptual point of view, the main feature of our approach is its high level of unification: while the notions of source, choice of setting and measurement play all seemingly different roles in a Bell scenario, our formalism shows that they are all instances of the same concept of "event". Our work can also be understood as a contribution to the subject of causal inference with latent variables. Among other things, we introduce hidden Bayesian networks as a generalization of hidden Markov models.

Approximate Newton methods are a standard optimization tool which aim to maintain the benefits of Newton's method, such as a fast rate of convergence, whilst alleviating its drawbacks, such as computationally expensive calculation or estimation of the inverse Hessian. In this work we investigate approximate Newton methods for policy optimization in Markov Decision Processes (MDPs). We first analyse the structure of the Hessian of the objective function for MDPs. We show that, like the gradient, the Hessian exhibits useful structure in the context of MDPs and we use this analysis to motivate two Gauss-Newton Methods for MDPs. Like the Gauss-Newton method for non-linear least squares, these methods involve approximating the Hessian by ignoring certain terms in the Hessian which are difficult to estimate. The approximate Hessians possess desirable properties, such as negative definiteness, and we demonstrate several important performance guarantees including guaranteed ascent directions, invariance to affine transformation of the parameter space, and convergence guarantees. We finally provide a unifying perspective of key policy search algorithms, demonstrating that our second Gauss-Newton algorithm is closely related to both the EM-algorithm and natural gradient ascent applied to MDPs, but performs significantly better in practice on a range of challenging domains.

With different genomes available, unsupervised learning algorithms are essential in learning genome-wide biological insights. Especially, the functional characterization of different genomes is essential for us to understand lives. In this book chapter, we review the state-of-the-art unsupervised learning algorithms for genome informatics from DNA to MicroRNA. DNA (DeoxyriboNucleic Acid) is the basic component of genomes. A significant fraction of DNA regions (transcription factor binding sites) are bound by proteins (transcription factors) to regulate gene expression at different development stages in different tissues. To fully understand genetics, it is necessary of us to apply unsupervised learning algorithms to learn and infer those DNA regions. Here we review several unsupervised learning methods for deciphering the genome-wide patterns of those DNA regions. MicroRNA (miRNA), a class of small endogenous non-coding RNA (RiboNucleic acid) species, regulate gene expression post-transcriptionally by forming imperfect base-pair with the target sites primarily at the 3$'$ untranslated regions of the messenger RNAs. Since the 1993 discovery of the first miRNA \emph{let-7} in worms, a vast amount of studies have been dedicated to functionally characterizing the functional impacts of miRNA in a network context to understand complex diseases such as cancer. Here we review several representative unsupervised learning frameworks on inferring miRNA regulatory network by exploiting the static sequence-based information pertinent to the prior knowledge of miRNA targeting and the dynamic information of miRNA activities implicated by the recently available large data compendia, which interrogate genome-wide expression profiles of miRNAs and/or mRNAs across various cell conditions.

We define a Hidden Markov Model (HMM) in which each hidden state has time-dependent $\textit{activity levels}$ that drive transitions and emissions, and show how to estimate its parameters. Our construction is motivated by the problem of inferring human mobility on sub-daily time scales from, for example, mobile phone records.

We have recently shown that deep Long Short-Term Memory (LSTM) recurrent neural networks (RNNs) outperform feed forward deep neural networks (DNNs) as acoustic models for speech recognition. More recently, we have shown that the performance of sequence trained context dependent (CD) hidden Markov model (HMM) acoustic models using such LSTM RNNs can be equaled by sequence trained phone models initialized with connectionist temporal classification (CTC). In this paper, we present techniques that further improve performance of LSTM RNN acoustic models for large vocabulary speech recognition. We show that frame stacking and reduced frame rate lead to more accurate models and faster decoding. CD phone modeling leads to further improvements. We also present initial results for LSTM RNN models outputting words directly.