Bayesian probabilistic models provide a nimble and expressive framework for modeling "small-world" data. In contrast, deep learning offers a more rigid yet much more powerful framework for modeling data of massive size. Edward is a probabilistic programming library that bridges this gap: "black-box" variational inference enables us to fit extremely flexible Bayesian models to large-scale data. Furthermore, these models themselves may take advantage of classic deep-learning architectures of arbitrary complexity. Edward uses TensorFlow for symbolic gradients and data flow graphs.

Most tasks in Machine Learning can be reduced to classification tasks. For example, we have a medical dataset and we want to classify who has diabetes (positive class) and who doesn't (negative class). We have a dataset from the financial world and want to know which customers will default on their credit (positive class) and which customers will not (negative class). To do this, we can train a Classifier with a'training dataset' and after such a Classifier is trained (we have determined its model parameters) and can accurately classify the training set, we can use it to classify new data (test set). If the training is done properly, the Classifier should predict the class probabilities of the new data with a similar accuracy.

This paper introduces DeepBach, a graphical model aimed at modeling polyphonic music and specifically hymn-like pieces. We claim that, after being trained on the chorale harmonizations by Johann Sebastian Bach, our model is capable of generating highly convincing chorales in the style of Bach. DeepBach's strength comes from the use of pseudo-Gibbs sampling coupled with an adapted representation of musical data. This is in contrast with many automatic music composition approaches which tend to compose music sequentially. Our model is also steerable in the sense that a user can constrain the generation by imposing positional constraints such as notes, rhythms or cadences in the generated score. We also provide a plugin on top of the MuseScore music editor making the interaction with Deep-Bach easy to use.

Traditional GANs use a deterministic generator function (typically a neural network) to transform a random noise input $z$ to a sample $\mathbf{x}$ that the discriminator seeks to distinguish. We propose a new GAN called Bayesian Conditional Generative Adversarial Networks (BC-GANs) that use a random generator function to transform a deterministic input $y'$ to a sample $\mathbf{x}$. Our BC-GANs extend traditional GANs to a Bayesian framework, and naturally handle unsupervised learning, supervised learning, and semi-supervised learning problems. Experiments show that the proposed BC-GANs outperforms the state-of-the-arts.

In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive results are developed on both the statistical and computational limits for tensor SVD. This problem exhibits three different phases according to the signal-noise-ratio (SNR). In particular, with strong SNR, we show that the classical higher order orthogonal iteration achieves the minimax optimal rate of convergence in estimation; with weak SNR, the information-theoretical lower bound implies that it is impossible to have consistent estimation in general; with moderate SNR, we show that the non-convex maximum likelihood estimation provides optimal solution, but with NP-hard computational cost; moreover, under the hardness hypothesis of hypergraphic planted clique detection, there are no polynomial-time algorithms performing consistently in general.

Generative models have long been the dominant approach for speech recognition. The success of these models however relies on the use of sophisticated recipes and complicated machinery that is not easily accessible to non-practitioners. Recent innovations in Deep Learning have given rise to an alternative - discriminative models called Sequence-to-Sequence models, that can almost match the accuracy of state of the art generative models. While these models are easy to train as they can be trained end-to-end in a single step, they have a practical limitation that they can only be used for offline recognition. This is because the models require that the entirety of the input sequence be available at the beginning of inference, an assumption that is not valid for instantaneous speech recognition. To address this problem, online sequence-to-sequence models were recently introduced. These models are able to start producing outputs as data arrives, and the model feels confident enough to output partial transcripts. These models, like sequence-to-sequence are causal - the output produced by the model until any time, $t$, affects the features that are computed subsequently. This makes the model inherently more powerful than generative models that are unable to change features that are computed from the data. This paper highlights two main contributions - an improvement to online sequence-to-sequence model training, and its application to noisy settings with mixed speech from two speakers.

In an earlier blog, "Need for DYNAMICAL Machine Learning: Bayesian exact recursive estimation", I introduced the need for Dynamical ML as we now enter the "Walk" stage of "Crawl-Walk-Run" evolution of machine learning. First, I defined Static ML as follows: Given a set of inputs and outputs, find a static map between the two during supervised "Training" and use this static map for business purposes during "Operation". I made the following points using IoT as an example. Dynamical ML solution involves State-Space data model (more below). What more does a Dynamical ML solution offer?

We present a probabilistic framework for overlapping community discovery and link prediction for relational data, given as a graph. The proposed framework has: (1) a deep architecture which enables us to infer multiple layers of latent features/communities for each node, providing superior link prediction performance on more complex networks and better interpretability of the latent features; and (2) a regression model which allows directly conditioning the node latent features on the side information available in form of node attributes. Our framework handles both (1) and (2) via a clean, unified model, which enjoys full local conjugacy via data augmentation, and facilitates efficient inference via closed form Gibbs sampling. Moreover, inference cost scales in the number of edges which is attractive for massive but sparse networks. Our framework is also easily extendable to model weighted networks with count-valued edges. We compare with various state-of-the-art methods and report results, both quantitative and qualitative, on several benchmark data sets.

Many modern data sets are sampled with error from complex high-dimensional surfaces. Methods such as tensor product splines or Gaussian processes are effective/well suited for characterizing a surface in two or three dimensions but may suffer from difficulties when representing higher dimensional surfaces. Motivated by high throughput toxicity testing where observed dose-response curves are cross sections of a surface defined by a chemical's structural properties, a model is developed to characterize this surface to predict untested chemicals' dose-responses. This manuscript proposes a novel approach that models the multidimensional surface as a sum of learned basis functions formed as the tensor product of lower dimensional functions, which are themselves representable by a basis expansion learned from the data. The model is described, a Gibbs sampling algorithm proposed, and is investigated in a simulation study as well as data taken from the US EPA's ToxCast high throughput toxicity testing platform.

An implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs is described. A hierarchical Bayesian approach with a randomly scaled Gaussian prior is considered. The prior uses the graph Laplacian to take into account the underlying geometry of the graph. A method based on a theoretically optimal prior and a more flexible variant using partial conjugacy are proposed. Two simulated data examples and two examples using real data are used in order to illustrate the proposed methods.