Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for theories which encompass our understanding of the physical world. Despite this fundamental nature, the use of implicit models remains limited due to challenges in specifying complex latent structure in them, and in performing inferences in such models with large data sets.

Parviainen et al. (2014) adopted an anytime integer linear programming (ILP) Otherwise it returns a sub-optimal DAG with bounded treewidth. Nie et al. (2014) proposed an efficient anytime ILP approach with a polynomial number of constraints Nie et al. (2015) proposed the method S2.

Predicated on the increasing abundance of electronic health records, we investigate the problem of inferring individualized treatment effects using observational data. Stemming from the potential outcomes model, we propose a novel multi-task learning framework in which factual and counterfactual outcomes are modeled as the outputs of a function in a vector-valued reproducing kernel Hilbert space (vvRKHS). We develop a nonparametric Bayesian method for learning the treatment effects using a multi-task Gaussian process (GP) with a linear coregion-alization kernel as a prior over the vvRKHS. The Bayesian approach allows us to compute individualized measures of confidence in our estimates via pointwise credible intervals, which are crucial for realizing the full potential of precision medicine. The impact of selection bias is alleviated via a risk-based empirical Bayes method for adapting the multi-task GP prior, which jointly minimizes the empirical error in factual outcomes and the uncertainty in (unobserved) counterfactual outcomes. We conduct experiments on observational datasets for an inter-ventional social program applied to premature infants, and a left ventricular assist device applied to cardiac patients wait-listed for a heart transplant. In both experiments, we show that our method significantly outperforms the state-of-the-art.

Neural Information Processing Systems http://nips.cc/

The marginal likelihood, or model evidence, is a key quantity in Bayesian parameter estimation and model comparison.

Conditional probabilities are a core concept in machine learning.

One use of such an estimate is to evaluate risk; e.g. is this patient likely to die if I do not

A new model, named as deep dynamic poisson factorization model, is proposed in this paper for analyzing sequential count vectors.

In this paper, we present two algorithms of this type and prove that both are consistent under the faithfulness assumption.

Generalized linear models (GLMs)--such as logistic regression, Poisson regression, and robust regression--provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent estimates of uncertainty, incorporation of prior information, and sharing of power across experiments via hierarchical models. In practice, however, the approximate Bayesian methods necessary for inference have either failed to scale to large data sets or failed to provide theoretical guarantees on the quality of inference. We propose a new approach based on constructing polynomial approximate sufficient statistics for GLMs (P ASS-GLM). We demonstrate that our method admits a simple algorithm as well as trivial streaming and distributed extensions that do not compound error across computations. We provide theoretical guarantees on the quality of point (MAP) estimates, the approximate posterior, and posterior mean and uncertainty estimates. We validate our approach empirically in the case of logistic regression using a quadratic approximation and show competitive performance with stochastic gradient descent, MCMC, and the Laplace approximation in terms of speed and multiple measures of accuracy--including on an advertising data set with 40 million data points and 20,000 covariates.