Probabilistic programming languages (PPLs) are a powerful modeling tool, able to represent any computable probability distribution. Unfortunately, probabilistic program inference is often intractable, and existing PPLs mostly rely on expensive, approximate sampling-based methods. To alleviate this problem, one could try to learn from past inferences, so that future inferences run faster. This strategy is known as amortized inference; it has recently been applied to Bayesian networks and deep generative models. This paper proposes a system for amortized inference in PPLs. In our system, amortization comes in the form of a parameterized guide program. Guide programs have similar structure to the original program, but can have richer data flow, including neural network components. These networks can be optimized so that the guide approximately samples from the posterior distribution defined by the original program. We present a flexible interface for defining guide programs and a stochastic gradient-based scheme for optimizing guide parameters, as well as some preliminary results on automatically deriving guide programs. We explore in detail the common machine learning pattern in which a 'local' model is specified by 'global' random values and used to generate independent observed data points; this gives rise to amortized local inference supporting global model learning.

Learning has become an online activity - people routinely use a wide variety of online learning platforms, ranging from wikis and question answering (Q&A) sites to online communities and blogs, to learn about a large range of topics. In this context, people find solutions to their problems by looking for closely related pieces of information, executing a sequence of queries or, more generally, performing a series of online actions. For example, a high school student may study several closely related wiki pages to prepare an essay about a historical event; a software developer may read several answers within a Q&A site to solve a specific programming problem; and, a researcher may check a specialized blog written by one of her peers to learn about a new concept or technique. All the above are examples of learning patterns, in which people perform a series of online actions - reading a wiki page, an answer, or a blog - to achieve a predefined goal - writing an essay, solving a programming problem, or learning about a new concept or technique. In this context, one may expect that people with similar goals undertake similar sequences of online actions and thus adopt similar learning patterns. Therefore, one could leverage the vast availability of online traces of users' learning activity to disambiguate among interleaved learning patterns adopted by individuals over time, as well as to automatically identify and track those people's interests and goals over time. In this work, we introduce a novel probabilistic model, the Hierarchical Dirichlet Hawkes Process (HDHP), for clustering continuous-time grouped streaming data, which we use to uncover the dynamics of learning activity on the web. The HDHP leverages the properties of the Hierarchical Dirichlet Process (HDP) [18], a popular Bayesian nonparametric model for clustering problems involving multiple groups of data, combined with the Hawkes process [13], a temporal point process particularly well fitted to model social activity [11, 19, 20]. In particular, the former is used to account for an infinite number of learning patterns, which are shared across users (groups) of an online learning platform.

This paper presents an asynchronous incremental aggregated gradient algorithm and its implementation in a parameter server framework for solving regularized optimization problems. The algorithm can handle both general convex (possibly non-smooth) regularizers and general convex constraints. When the empirical data loss is strongly convex, we establish linear convergence rate, give explicit expressions for step-size choices that guarantee convergence to the optimum, and bound the associated convergence factors. The expressions have an explicit dependence on the degree of asynchrony and recover classical results under synchronous operation. Simulations and implementations on commercial compute clouds validate our findings.

We study model evaluation and model selection from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. We believe that GA is one way formally to address concerns about the external validity of a model. The GA of a model estimated on a sample can be measured by its empirical out-of-sample errors, called the generalization errors (GE). We derive upper bounds for the GE, which depend on sample sizes, model complexity and the distribution of the loss function. The upper bounds can be used to evaluate the GA of a model, ex ante. We propose using generalization error minimization (GEM) as a framework for model selection. Using GEM, we are able to unify a big class of penalized regression estimators, including lasso, ridge and bridge, under the same set of assumptions. We establish finite-sample and asymptotic properties (including $\mathcal{L}_2$-consistency) of the GEM estimator for both the $n \geqslant p$ and the $n < p$ cases. We also derive the $\mathcal{L}_2$-distance between the penalized and corresponding unpenalized regression estimates. In practice, GEM can be implemented by validation or cross-validation. We show that the GE bounds can be used for selecting the optimal number of folds in $K$-fold cross-validation. We propose a variant of $R^2$, the $GR^2$, as a measure of GA, which considers both both in-sample and out-of-sample goodness of fit. Simulations are used to demonstrate our key results.

We investigate metric learning in the context of dynamic time warping (DTW), the by far most popular dissimilarity measure used for the comparison and analysis of motion capture data. While metric learning enables a problem-adapted representation of data, the majority of meth- ods has been proposed for vectorial data only. In this contribution, we extend the popular principle offered by the large margin nearest neighbours learner (LMNN) to DTW by treating the resulting component-wise dissimilarity values as features. We demonstrate, that this principle greatly enhances the classification accuracy in several benchmarks. Further, we show that recent auxiliary concepts such as metric regularisation can be transferred from the vectorial case to component-wise DTW in a similar way. We illustrate, that metric regularisation constitutes a crucial prerequisite for the interpretation of the resulting relevance profiles.

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian modeling and predictive strengths of max-margin learning. However, Monte Carlo sampling for these models still remains challenging, especially for applications that involve large-scale datasets. In this paper, we present the stochastic subgradient Hamiltonian Monte Carlo (HMC) methods, which are easy to implement and computationally efficient. We show the approximate detailed balance property of subgradient HMC which reveals a natural and validated generalization of the ordinary HMC. Furthermore, we investigate the variants that use stochastic subsampling and thermostats for better scalability and mixing. Using stochastic subgradient Markov Chain Monte Carlo (MCMC), we efficiently solve the posterior inference task of various Bayesian max-margin models and extensive experimental results demonstrate the effectiveness of our approach.

If you are modeling binomial data; ie a numerator consisting of the number of 1/0 successes you have for a given pattern of covariates, and a denominator that gives the value of the total number of observations having that covariate pattern (a specific profile of predictor values; eg age 23, married 1, working 0), a logistic regresson is generally appropriate. But when the mean values of the numerators are less than 10% of the mean values of the denominator, it is likely that a Poisson model is preferred. The otherwise logistic numerator is the count response variable (dependent variable) and the natural log of the denominator is the offset. Generally the Poisson model will fit the data better. Logistic models are not indended for rare occurrences.

Cluster analysis is a staple of unsupervised machine learning and data science. It is very useful for data mining and big data because it automatically finds patterns in the data, without the need for labels, unlike supervised machine learning. In a real-world environment, you can imagine that a robot or an artificial intelligence won't always have access to the optimal answer, or maybe there isn't an optimal correct answer. You'd want that robot to be able to explore the world on its own, and learn things just by looking for patterns. Do you ever wonder how we get the data that we use in our supervised machine learning algorithms?

Quantitative modeling of post-transcriptional regulation process is a challenging problem in systems biology. A mechanical model of the regulatory process needs to be able to describe the available spatio-temporal protein concentration and mRNA expression data and recover the continuous spatio-temporal fields. Rigorous methods are required to identify model parameters. A promising approach to deal with these difficulties is proposed using Gaussian process as a prior distribution over the latent function of protein concentration and mRNA expression. In this study, we consider a partial differential equation mechanical model with differential operators and latent function. Since the operators at stake are linear, the information from the physical model can be encoded into the kernel function. Hybrid Monte Carlo methods are employed to carry out Bayesian inference of the partial differential equation parameters and Gaussian process kernel parameters. The spatio-temporal field of protein concentration and mRNA expression are reconstructed without explicitly solving the partial differential equation.

Importance sampling is widely used in machine learning and statistics, but its power is limited by the restriction of using simple proposals for which the importance weights can be tractably calculated. We address this problem by studying black-box importance sampling methods that calculate importance weights for samples generated from any unknown proposal or black-box mechanism. Our method allows us to use better and richer proposals to solve difficult problems, and (somewhat counter-intuitively) also has the additional benefit of improving the estimation accuracy beyond typical importance sampling. Both theoretical and empirical analyses are provided.