This paper introduces the probabilistic module interface, which allows encapsulation of complex probabilistic models with latent variables alongside custom stochastic approximate inference machinery, and provides a platform-agnostic abstraction barrier separating the model internals from the host probabilistic inference system. The interface can be seen as a stochastic generalization of a standard simulation and density interface for probabilistic primitives. We show that sound approximate inference algorithms can be constructed for networks of probabilistic modules, and we demonstrate that the interface can be implemented using learned stochastic inference networks and MCMC and SMC approximate inference programs.

As manufacturing processes become increasingly automated, so should tool condition monitoring (TCM) as it is impractical to have human workers monitor the state of the tools continuously. Tool condition is crucial to ensure the good quality of products: Worn tools affect not only the surface quality but also the dimensional accuracy, which means higher reject rate of the products. Therefore, there is an urgent need to identify tool failures before it occurs on the fly. While various versions of intelligent tool condition monitoring have been proposed, most of them suffer from a cognitive nature of traditional machine learning algorithms. They focus on the how to learn process without paying attention to other two crucial issues: what to learn, and when to learn. The what to learn and the when to learn provide self regulating mechanisms to select the training samples and to determine time instants to train a model. A novel tool condition monitoring approach based on a psychologically plausible concept, namely the metacognitive scaffolding theory, is proposed and built upon a recently published algorithm, recurrent classifier (rClass). The learning process consists of three phases: what to learn, how to learn, when to learn and makes use of a generalized recurrent network structure as a cognitive component. Experimental studies with real-world manufacturing data streams were conducted where rClass demonstrated the highest accuracy while retaining the lowest complexity over its counterparts.

Gaussian Processes (GPs) are a popular approach to predict the output of a parameterized experiment. They have many applications in the field of Computer Experiments, in particular to perform sensitivity analysis, adaptive design of experiments and global optimization. Nearly all of the applications of GPs require the inversion of a covariance matrix that, in practice, is often ill-conditioned. Regularization methodologies are then employed with consequences on the GPs that need to be better understood.The two principal methods to deal with ill-conditioned covariance matrices are i) pseudoinverse and ii) adding a positive constant to the diagonal (the so-called nugget regularization).The first part of this paper provides an algebraic comparison of PI and nugget regularizations. Redundant points, responsible for covariance matrix singularity, are defined. It is proven that pseudoinverse regularization, contrarily to nugget regularization, averages the output values and makes the variance zero at redundant points. However, pseudoinverse and nugget regularizations become equivalent as the nugget value vanishes. A measure for data-model discrepancy is proposed which serves for choosing a regularization technique.In the second part of the paper, a distribution-wise GP is introduced that interpolates Gaussian distributions instead of data points. Distribution-wise GP can be seen as an improved regularization method for GPs.

In this paper we use Gaussian Process (GP) regression to propose a novel approach for predicting volatility of financial returns by forecasting the envelopes of the time series. We provide a direct comparison of their performance to traditional approaches such as GARCH. We compare the forecasting power of three approaches: GP regression on the absolute and squared returns; regression on the envelope of the returns and the absolute returns; and regression on the envelope of the negative and positive returns separately. We use a maximum a posteriori estimate with a Gaussian prior to determine our hyperparameters. We also test the effect of hyperparameter updating at each forecasting step. We use our approaches to forecast out-of-sample volatility of four currency pairs over a 2 year period, at half-hourly intervals. From three kernels, we select the kernel giving the best performance for our data. We use two published accuracy measures and four statistical loss functions to evaluate the forecasting ability of GARCH vs GPs. In mean squared error the GP's perform 20% better than a random walk model, and 50% better than GARCH for the same data.

One aspect I always enjoy about machine learning is that questions often go back to the basics. The field essentially goes into an existential crisis every dozen years--rethinking our tools and asking foundational questions such as "why neural networks" or "why generative models".1 This was a theme in my conversations during NIPS 2016 last week, where a frequent topic was on the advantages of a Bayesian perspective to machine learning. Not surprisingly, this appeared as a big discussion point during the panel at the Bayesian deep learning workshop, where many panelists were conciliatory to the use of non-Bayesian approaches. While Bayesian inference can capture uncertainty about parameters, it relies on the model being correctly specified.

We consider the inference of the structure of an undirected graphical model in an exact Bayesian framework. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. This task would be intractable without any restriction on the considered graphs, so we limit our exploration to mixtures of spanning trees. We consider the inference of the structure of an undirected graphical model in a Bayesian framework. To avoid convergence issues and highly demanding Monte Carlo sampling, we focus on exact inference. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. To this aim, we restrict the set of considered graphs to mixtures of spanning trees. We investigate under which conditions on the priors - on both tree structures and parameters - exact Bayesian inference can be achieved. Under these conditions, we derive a fast an exact algorithm to compute the posterior probability for an edge to belong to {the tree model} using an algebraic result called the Matrix-Tree theorem. We show that the assumption we have made does not prevent our approach to perform well on synthetic and flow cytometry data.

Multi-label text classification is a popular machine learning task where each document is assigned with multiple relevant labels. This task is challenging due to high dimensional features and correlated labels. Multi-label text classifiers need to be carefully regularized to prevent the severe over-fitting in the high dimensional space, and also need to take into account label dependencies in order to make accurate predictions under uncertainty. We demonstrate significant and practical improvement by carefully regularizing the model complexity during training phase, and also regularizing the label search space during prediction phase. Specifically, we regularize the classifier training using Elastic-net (L1+L2) penalty for reducing model complexity/size, and employ early stopping to prevent overfitting. At prediction time, we apply support inference to restrict the search space to label sets encountered in the training set, and F-optimizer GFM to make optimal predictions for the F1 metric. We show that although support inference only provides density estimations on existing label combinations, when combined with GFM predictor, the algorithm can output unseen label combinations. Taken collectively, our experiments show state of the art results on many benchmark datasets. Beyond performance and practical contributions, we make some interesting observations. Contrary to the prior belief, which deems support inference as purely an approximate inference procedure, we show that support inference acts as a strong regularizer on the label prediction structure. It allows the classifier to take into account label dependencies during prediction even if the classifiers had not modeled any label dependencies during training.

We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood. In this paper we propose novel algorithms to optimize the forward and reverse forms of the KL divergence, as well as the alpha-divergence which contains these two as limiting cases. Unlike previous approaches, our algorithms do not make approximations to the divergences being optimized, but use Monte Carlo integration techniques to derive unbiased algorithms for direct optimization. We assess performance on radar and sensor tracking, and options pricing problems, showing general improvement over the UKF and EKF, as well as competitive performance with particle filtering.

Despite the promise of big data, inferences are often limited not by sample size but rather by systematic effects. Only by carefully modeling these effects can we take full advantage of the data--big data must be complemented with big models and the algorithms that can fit them. One such algorithm is Hamiltonian Monte Carlo, which exploits the inherent geometry of the posterior distribution to admit full Bayesian inference that scales to the complex models of practical interest. In this talk I will discuss the theoretical foundations of Hamiltonian Monte Carlo, elucidating the geometric nature of its scalable performance and stressing the properties critical to a robust implementation. The talk is this Thurs, 6 Apr, 1:10-2:20pm in 303 Mudd Building at Columbia.

As the emergence and the thriving development of social networks, a huge number of short texts are accumulated and need to be processed. Inferring latent topics of collected short texts is useful for understanding its hidden structure and predicting new contents. Unlike conventional topic models such as latent Dirichlet allocation (LDA), a biterm topic model (BTM) was recently proposed for short texts to overcome the sparseness of document-level word co-occurrences by directly modeling the generation process of word pairs. Stochastic inference algorithms based on collapsed Gibbs sampling (CGS) and collapsed variational inference have been proposed for BTM. However, they either require large computational complexity, or rely on very crude estimation. In this work, we develop a stochastic divergence minimization inference algorithm for BTM to estimate latent topics more accurately in a scalable way. Experiments demonstrate the superiority of our proposed algorithm compared with existing inference algorithms.