We address the problem of deciding whether a causal or probabilistic query is estimable from data corrupted by missing entries, given a model of missingness process.We extend the results of Mohan et al. [2013] by presenting more general conditions for recovering probabilistic queries of the form P(y x) and P(y,x) as well as causal queries of the form P(y do(x)). We show that causal queries may be recoverable even when the factors in their identifying estimands are not recoverable. Specifically, we derive graphical conditions for recovering causal effects of the form P(y do(x)) when Y and its missingness mechanism are not d-separable. Finally, we apply our results toproblems of attrition and characterize the recovery of causal effects from data corrupted by attrition.

This paper studies the problem of rank aggregation under the Plackett-Luce model. The goal is to infer a global ranking and related scores of the items, based on partial rankings provided by multiple users over multiple subsets of items. A question of particular interest is how to optimally assign items to users for ranking and how many item assignments are needed to achieve a target estimation error. Without any assumptions on how the items are assigned to users, we derive an oracle lower bound and the Cram\'er-Rao lower bound of the estimation error. We prove an upper bound on the estimation error achieved by the maximum likelihood estimator, and show that both the upper bound and the Cram\'er-Rao lower bound inversely depend on the spectral gap of the Laplacian of an appropriately defined comparison graph. Since random comparison graphs are known to have large spectral gaps, this suggests the use of random assignments when we have the control. Precisely, the matching oracle lower bound and the upper bound on the estimation error imply that the maximum likelihood estimator together with a random assignment is minimax-optimal up to a logarithmic factor. We further analyze a popular rank-breaking scheme that decompose partial rankings into pairwise comparisons. We show that even if one applies the mismatched maximum likelihood estimator that assumes independence (on pairwise comparisons that are now dependent due to rank-breaking), minimax optimal performance is still achieved up to a logarithmic factor.

Bayesian observer models are very effective in describing human performance in perceptual tasks, so much so that they are trusted to faithfully recover hidden mental representations of priors, likelihoods, or loss functions from the data. However, the intrinsic degeneracy of the Bayesian framework, as multiple combinations of elements can yield empirically indistinguishable results, prompts the question of model identifiability. We propose a novel framework for a systematic testing of the identifiability of a significant class of Bayesian observer models, with practical applications for improving experimental design. We examine the theoretical identifiability of the inferred internal representations in two case studies. First, we show which experimental designs work better to remove the underlying degeneracy in a time interval estimation task. Second, we find that the reconstructed representations in a speed perception task under a slow-speed prior are fairly robust.

Coverage functions are an important class of discrete functions that capture the law of diminishing returns arising naturally from applications in social network analysis, machine learning, and algorithmic game theory. In this paper, we propose anew problem of learning time-varying coverage functions, and develop a novel parametrization of these functions using random features. Based on the connection betweentime-varying coverage functions and counting processes, we also propose an efficient parameter learning algorithm based on likelihood maximization, andprovide a sample complexity analysis. We applied our algorithm to the influence function estimation problem in information diffusion in social networks, and show that with few assumptions about the diffusion processes, our algorithm is able to estimate influence significantly more accurately than existing approaches on both synthetic and real world data.

Implementing inference procedures for each new probabilistic model is timeconsuming anderror-prone. Probabilistic programming addresses this problem by allowing a user to specify the model and then automatically generating the inference procedure. To make this practical it is important to generate high performance inferencecode. In turn, on modern architectures, high performance requires parallel execution. In this paper we present Augur, a probabilistic modeling language and compiler for Bayesian networks designed to make effective use of data-parallel architectures such as GPUs. We show that the compiler can generate data-parallel inference code scalable to thousands of GPU cores by making use of the conditional independence relationships in the Bayesian network.

We analyse a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For densities on the d-dimensional unit cube [0,1]^d that lie in a beta-Holder smoothness class, we prove our estimator converges at the rate O(n^(1/(beta+d))). Furthermore, we prove that the estimator obeys an exponential concentration inequality about its mean, whereas most previous related results have bounded only expected error of estimators. Finally, we demonstrate our bounds to the case of conditional Renyi mutual information.

We propose a multimodal retrieval procedure based on latent feature models. The procedure consists of a nonparametric Bayesian framework for learning underlying semantically meaningful abstract features in a multimodal dataset, a probabilistic retrieval model that allows cross-modal queries and an extension model for relevance feedback. Experiments on two multimodal datasets, PASCAL-Sentence and SUN-Attribute, demonstrate the effectiveness of the proposed retrieval procedure in comparison to the state-of-the-art algorithms for learning binary codes.

We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the global maximum. PES codifies this intractable acquisition function in terms of the expected reduction in the differential entropy of the predictive distribution. This reformulation allows PES to obtain approximations that are both more accurate and efficient than other alternatives such as Entropy Search (ES). Furthermore, PES can easily perform a fully Bayesian treatment of the model hyperparameters while ES cannot. We evaluate PES in both synthetic and real-world applications, including optimization problems in machine learning, finance, biotechnology, and robotics. We show that the increased accuracy of PES leads to significant gains in optimization performance.

The integration of partially redundant information from multiple sensors is a standard computational problem for agents interacting with the world. In man and other primates, integration has been shown psychophysically to be nearly optimal in the sense of error minimization. An influential generalization of this notion of optimality is that populations of multisensory neurons should retain all the information from their unisensory afferents about the underlying, common stimulus [1]. More recently, it was shown empirically that a neural network trained to perform latent-variable density estimation, with the activities of the unisensory neurons as observed data, satisfies the information-preservation criterion, even though the model architecture was not designed to match the true generative process for the data [2]. We prove here an analytical connection between these seemingly different tasks, density estimation and sensory integration; that the former implies the latter for the model used in [2]; but that this does not appear to be true for all models.

We present an inference method for Gaussian graphical models when only pairwise distances of n objects are observed. Formally, this is a problem of estimating an n x n covariance matrix from the Mahalanobis distances dMH(xi, xj), where object xi lives in a latent feature space. We solve the problem in fully Bayesian fashion by integrating over the Matrix-Normal likelihood and a Matrix-Gamma prior; the resulting Matrix-T posterior enables network recovery even under strongly correlated features. Hereby, we generalize TiWnet, which assumes Euclidean distances with strict feature independence. In spite of the greatly increased flexibility, our model neither loses statistical power nor entails more computational cost. We argue that the extension is highly relevant as it yields significantly better results in both synthetic and real-world experiments, which is successfully demonstrated for a network of biological pathways in cancer patients.