Causal Inference through a Witness Protection Program Machine Learning

One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been adjusted for. We introduce a novel approach for estimating causal effects that exploits observational conditional independencies to suggest "weak" paths in a unknown causal graph. The widely used faithfulness condition of Spirtes et al. is relaxed to allow for varying degrees of "path cancellations" that imply conditional independencies but do not rule out the existence of confounding causal paths. The outcome is a posterior distribution over bounds on the average causal effect via a linear programming approach and Bayesian inference. We claim this approach should be used in regular practice along with other default tools in observational studies.

PAC-Bayes Learning of Conjunctions and Classification of Gene-Expression Data

Neural Information Processing Systems

We propose a "soft greedy" learning algorithm for building small conjunctions of simple threshold functions, called rays, defined on single real-valued attributes. We also propose a PAC-Bayes risk bound which is minimized for classifiers achieving a nontrivial tradeoff between sparsity (the number of rays used) and the magnitude ofthe separating margin of each ray. Finally, we test the soft greedy algorithm on four DNA micro-array data sets.

Stable specification search in structural equation model with latent variables Machine Learning

In our previous study, we introduced stable specification search for cross-sectional data (S3C). It is an exploratory causal method that combines stability selection concept and multi-objective optimization to search for stable and parsimonious causal structures across the entire range of model complexities. In this study, we extended S3C to S3C-Latent, to model causal relations between latent variables. We evaluated S3C-Latent on simulated data and compared the results to those of PC-MIMBuild, an extension of the PC algorithm, the state-of-the-art causal discovery method. The comparison showed that S3C-Latent achieved better performance. We also applied S3C-Latent to real-world data of children with attention deficit/hyperactivity disorder and data about measuring mental abilities among pupils. The results are consistent with those of previous studies.

Priors over Recurrent Continuous Time Processes

Neural Information Processing Systems

We introduce the Gamma-Exponential Process (GEP), a prior over a large family ofcontinuous time stochastic processes. A hierarchical version of this prior (HGEP; the Hierarchical GEP) yields a useful model for analyzing complex time series. Models based on HGEPs display many attractive properties: conjugacy, exchangeability and closed-form predictive distribution for the waiting times, and exact Gibbs updates for the time scale parameters. After establishing these properties, weshow how posterior inference can be carried efficiently using Particle MCMC methods [1]. This yields a MCMC algorithm that can resample entire sequences atomicallywhile avoiding the complications of introducing slice and stick auxiliary variables of the beam sampler [2]. We applied our model to the problem of estimating the disease progression in multiple sclerosis [3], and to RNA evolutionary modeling[4]. In both domains, we found that our model outperformed the standard rate matrix estimation approach.

Transfer Learning Across Patient Variations with Hidden Parameter Markov Decision Processes Machine Learning

Due to physiological variation, patients diagnosed with the same condition may exhibit divergent, but related, responses to the same treatments. Hidden Parameter Markov Decision Processes (HiP-MDPs) tackle this transfer-learning problem by embedding these tasks into a low-dimensional space. However, the original formulation of HiP-MDP had a critical flaw: the embedding uncertainty was modeled independently of the agent's state uncertainty, requiring an unnatural training procedure in which all tasks visited every part of the state space---possible for robots that can be moved to a particular location, impossible for human patients. We update the HiP-MDP framework and extend it to more robustly develop personalized medicine strategies for HIV treatment.