In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed features is represented by a set of decomposable Gaussian graphical models. Emphasis is then placed on the Bayesian model averaging which takes full account of the class-specific model uncertainty by averaging over the posterior graph model probabilities. Even though the decomposability assumption severely reduces the model space, the size of the class of decomposable models is still immense, rendering the explicit Bayesian averaging over all the models infeasible. To address this issue, we consider the particle Gibbs strategy of Olsson et al. (2016) for posterior sampling from decomposable graphical models which utilizes the Christmas tree algorithm of Rios et al. (2016) as proposal kernel. We also derive the a strong hyper Markov law which we call the hyper normal Wishart law that allow to perform the resultant Bayesian calculations locally. The proposed predictive graphical classifier reveals superior performance compared to the ordinary Bayesian predictive rule that does not account for the model uncertainty, as well as to a number of out-of-the-box classifiers.

In assortment planning, the seller's goal is to select a subset of products (called an assortment) to offer to a customer so as to maximize the expected revenue. This task can be formulated as an optimization problem given the revenue generated from selling each product, along with a probabilistic model of the customer's preferences for the products. Such a discrete choice model must capture the customer's substitution behavior when, for instance, the offered assortment does not contain the customer's most preferred product. Our focus in this paper is the Markov chain choice model (MCCM) proposed by Blanchet et al. (2016). In this model, the product selected by the customer is determined by a Markov chain over products where the products in the offered assortment are absorbing states. The current state represents the desired product; if that product is not offered, the customer transitions to another product according to the Markov chain probabilities, and the process continues until the desired product is offered or the customer leaves. MCCM generalizes widely-used discrete choice models such as the multinomial logit model (Luce, 1959; Plackett, 1975), as well as other generalized attraction models (Gallego et al., 2014); it also well-approximates other random utility models found in the literature such as mixed multinomial logit models (McFadden and Train, 2000). At the same time, the MCCM permits computationally efficient unconstrained assortment optimization as well as efficient approximation algorithms in the constrained case (Blanchet et al., 2016; Désir et al., 2015); this stands in contrast to some richer models such as mixed multinomial logit models (Rusmevichientong et al., 2010) and the nested logit model (Davis et al., 2014) for which assortment optimization is generally intractable. This combination of expressiveness and computational tractability makes MCCM very attractive for use in assortment planning.

Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection methods. In sparse linear models, LASSO is well-known in extracting the desired support of the signal and resisting against noisy systems. When sparse models are also suffering from MI, the sparse recovery and inference of the missing models are taken into account simultaneously. In this paper, we will introduce an approach which enjoys sparse regression and covariance matrix estimation to improve matrix completion accuracy, and as a result enhancing feature selection preciseness which leads to reduction in prediction Mean Squared Error (MSE). We will compare the effect of employing covariance matrix in enhancing estimation accuracy to the case it is not used in feature selection. Simulations show the improvement in the performance as compared to the case where the covariance matrix estimation is not used.

This work falls within the context of predicting the value of a real function at some input locations given a limited number of observations of this function. The Kriging interpolation technique (or Gaussian process regression) is often considered to tackle such a problem but the method suffers from its computational burden when the number of observation points is large. We introduce in this article nested Kriging predictors which are constructed by aggregating sub-models based on subsets of observation points. This approach is proven to have better theoretical properties than other aggregation methods that can be found in the literature. Contrarily to some other methods it can be shown that the proposed aggregation method is consistent. Finally, the practical interest of the proposed method is illustrated on simulated datasets and on an industrial test case with $10^4$ observations in a 6-dimensional space.

We propose kernel sequential Monte Carlo (KSMC), a framework for sampling from static target densities. KSMC is a family of sequential Monte Carlo algorithms that are based on building emulator models of the current particle system in a reproducing kernel Hilbert space. We here focus on modelling nonlinear covariance structure and gradients of the target. The emulator's geometry is adaptively updated and subsequently used to inform local proposals. Unlike in adaptive Markov chain Monte Carlo, continuous adaptation does not compromise convergence of the sampler. KSMC combines the strengths of sequental Monte Carlo and kernel methods: superior performance for multimodal targets and the ability to estimate model evidence as compared to Markov chain Monte Carlo, and the emulator's ability to represent targets that exhibit high degrees of nonlinearity. As KSMC does not require access to target gradients, it is particularly applicable on targets whose gradients are unknown or prohibitively expensive. We describe necessary tuning details and demonstrate the benefits of the the proposed methodology on a series of challenging synthetic and real-world examples.

Approximate Bayesian Computation (ABC) is a method to obtain a posterior distribution without a likelihood function, using simulations and a set of distance metrics. For that reason, it has recently been gaining popularity as an analysis tool in cosmology and astrophysics. Its drawback, however, is a slow convergence rate. We propose a novel method, which we call qABC, to accelerate ABC with Quantile Regression. In this method, we create a model of quantiles of distance measure as a function of input parameters. This model is trained on a small number of simulations and estimates which regions of the prior space are likely to be accepted into the posterior. Other regions are then immediately rejected. This procedure is then repeated as more simulations are available. We apply it to the practical problem of estimation of redshift distribution of cosmological samples, using forward modelling developed in previous work. The qABC method converges to nearly same posterior as the basic ABC. It uses, however, only 20\% of the number of simulations compared to basic ABC, achieving a fivefold gain in execution time for our problem. For other problems the acceleration rate may vary; it depends on how close the prior is to the final posterior. We discuss possible improvements and extensions to this method.

Deep models are the defacto standard in visual decision models due to their impressive performance on a wide array of visual tasks. However, they are frequently seen as opaque and are unable to explain their decisions. In contrast, humans can justify their decisions with natural language and point to the evidence in the visual world which led to their decisions. We postulate that deep models can do this as well and propose our Pointing and Justification (PJ-X) model which can justify its decision with a sentence and point to the evidence by introspecting its decision and explanation process using an attention mechanism. Unfortunately there is no dataset available with reference explanations for visual decision making. We thus collect two datasets in two domains where it is interesting and challenging to explain decisions. First, we extend the visual question answering task to not only provide an answer but also a natural language explanation for the answer. Second, we focus on explaining human activities which is traditionally more challenging than object classification. We extensively evaluate our PJ-X model, both on the justification and pointing tasks, by comparing it to prior models and ablations using both automatic and human evaluations.

We propose to use thought-provoking children's questions (TPCQs), namely Highlights BrainPlay questions, as a new method to drive artificial intelligence research and to evaluate the capabilities of general-purpose AI systems. These questions are designed to stimulate thought and learning in children, and they can be used to do the same thing in AI systems, while demonstrating the system's reasoning capabilities to the evaluator. We introduce the TPCQ task, which which takes a TPCQ question as input and produces as output (1) answers to the question and (2) learned generalizations. We discuss how BrainPlay questions stimulate learning. We analyze 244 BrainPlay questions, and we report statistics on question type, question class, answer cardinality, answer class, types of knowledge needed, and types of reasoning needed. We find that BrainPlay questions span many aspects of intelligence. Because the answers to BrainPlay questions and the generalizations learned from them are often highly open-ended, we suggest using human judges for evaluation.

CrowdFlower, a company that helps customers build AI systems by providing them with training data, announced today that it's getting into the business of helping companies implement machine learning. While many companies are trying to incorporate AI and machine learning to further their business, there's a dearth of talent out there to help them get started. That's where CrowdFlower wants to come in, by providing support to get companies moving along the right path. "We're constantly being asked by our customers to give more guidance and play that trusted mentor role," CrowdFlower CEO Robin Bordoli said. "[Companies will say] well, we're thinking about the overall project, can you give us guidance on the overall project, not necessarily just the training data piece?'"

People with higher cognitive abilities are often better able to spot patterns in the world around them, allowing them to excel in a wide range of tasks, from learning languages to recognizing faces. But, in some situations, even being intelligent has its drawbacks. A new study has found that these people are more likely to stereotype others based on the patterns they detect, potentially leading to negative consequences as they perpetuate social biases. A new study found that people with higher cognitive abilities are more likely to stereotype others. In the study, the researchers manipulated image-description pairings so that the faces with particular features were linked to negative stereotypes.