In this paper we study the problem of making predictions using multiple structural casual models defined by different agents, under the constraint that the prediction satisfies the criterion of counterfactual fairness. Relying on the frameworks of causality, fairness and opinion pooling, we build upon and extend previous work focusing on the qualitative aggregation of causal Bayesian networks and causal models. In order to complement previous qualitative results, we devise a method based on Monte Carlo simulations. This method enables a decision-maker to aggregate the outputs of the causal models provided by different experts while guaranteeing the counterfactual fairness of the result. We demonstrate our approach on a simple, yet illustrative, toy case study.

Existing Bayesian treatments of neural networks are typically characterized by weak prior and approximate posterior distributions according to which all the weights are drawn independently. Here, we consider a richer prior distribution in which units in the network are represented by latent variables, and the weights between units are drawn conditionally on the values of the collection of those variables. This allows rich correlations between related weights, and can be seen as realizing a function prior with a Bayesian complexity regularizer ensuring simple solutions. We illustrate the resulting meta-representations and representations, elucidating the power of this prior.

MIT boffins reckon they can use old-school artificial intelligence to do much of the grunt work in the tricky task of picking suitable landing spots for spacecraft. The software uses fuzzy logic algorithms, which were introduced in the 1960s and were rather trendy in the 1990s. "Traditionally this idea comes from mathematics, where instead of saying an element belongs to a set, yes or no, fuzzy logic says it belongs with a certain probability, thus reflecting incomplete or imprecise information," Victor Pankratius, coauthor of the paper and a research scientist and principal investigator in NASA and National Science Foundation projects at MIT, explained this week. NASA and other space agencies have slowly amassed troves of geographical data on Mars. The researchers reckon that NASA has over 100 Terabits from all the different orbiters, landers, and rovers sent to the Red Planet, but it's still not enough to completely determine the exact conditions on the ground there.

Software defined networking (SDN) represents a promising networking architecture that combines central management and network programmability. SDN separates the control plane from the data plane and moves the network management to a central point, called the controller, that can be programmed and used as the brain of the network. Recently, the research community has showed an increased tendency to benefit from the recent advancements in the artificial intelligence (AI) field to provide learning abilities and better decision making in SDN. In this study, we provide a detailed overview of the recent efforts to include AI in SDN. Our study showed that the research efforts focused on three main sub-fields of AI namely: machine learning, meta-heuristics and fuzzy inference systems. Accordingly, in this work we investigate their different application areas and potential use, as well as the improvements achieved by including AI-based techniques in the SDN paradigm.

Abstract--In this paper we address the problem of tracking multiple speakers via the fusion of visual and auditory information. We propose to exploit the complementary nature of these two modalities in order to accurately estimate smooth trajectories of the tracked persons, to deal with the partial or total absence of one of the modalities over short periods of time, and to estimate the acoustic status - either speaking or silent - of each tracked person along time. We propose to cast the problem at hand into a generative audiovisual fusion (or association) model formulated as a latent-variable temporal graphical model. This may well be viewed as the problem of maximizing the posterior joint distribution of a set of continuous and discrete latent variables given the past and current observations, which is intractable. We propose a variational inference model which amounts to approximate the joint distribution with a factorized distribution. The solution takes the form of a closed-form expectation maximization procedure. We describe in detail the inference algorithm, we evaluate its performance and we compare it with several baseline methods. These experiments show that the proposed audiovisual tracker performs well in informal meetings involving a time-varying number of people. Index Terms--Audiovisual tracking, multiple object tracking, dynamic Bayesian networks, variational inference, expectationmaximization, speaker diarization. In this paper we address the problem of tracking multiple speakers via the fusion of visual and auditory information [1]- [7]. We propose to exploit the complementary nature of these two modalities in order to accurately estimate the position of each person at each time step, to deal with the partial or total absence of one of the modalities over short periods of time, and to estimate the acoustic status, either speaking or silent, of each tracked person. We propose to cast the problem at hand into a generative audiovisual fusion (or association) model formulated as a latent-variable temporal graphical model. We propose a tractable solver via a variational approximation.

Optimal treatment regimes (OTR) are individualised treatment assignment strategies that identify a medical treatment as optimal given all background information available on the individual. We discuss Bayes optimal treatment regimes estimated using a loss function defined on the bivariate distribution of dichotomous potential outcomes. The proposed approach allows considering more general objectives for the OTR than maximization of an expected outcome (e.g., survival probability) by taking into account, for example, unnecessary treatment burden. As a motivating example we consider the case of oropharynx cancer treatment where unnecessary burden due to chemotherapy is to be avoided while maximizing survival chances. Assuming ignorable treatment assignment we describe Bayesian inference about the OTR including a sensitivity analysis on the unobserved partial association of the potential outcomes. We evaluate the methodology by simulations that apply Bayesian parametric and more flexible non-parametric outcome models. The proposed OTR for oropharynx cancer reduces the frequency of the more burdensome chemotherapy assignment by approximately 75% without reducing the average survival probability. This regime thus offers a strong increase in expected quality of life of patients.

The theory of belief functions is widely used for data from multiple sources. Different evidence combination rules have been proposed in this framework according to the properties of the sources to combine. However, most of these combination rules are not efficient when there are a large number of sources. This is due to either the complexity or the existence of an absorbing element such as the total conflict mass function for the conjunctive based rules when applied on unreliable evidence. In this paper, based on the assumption that the majority of sources are reliable, a combination rule for a large number of sources is proposed using a simple idea: the more common ideas the sources share, the more reliable these sources are supposed to be. This rule is adaptable for aggregating a large number of sources which may not all be reliable. It will keep the spirit of the conjunctive rule to reinforce the belief on the focal elements with which the sources are in agreement. The mass on the emptyset will be kept as an indicator of the conflict. The proposed rule, called LNS-CR (Conjunctive combinationRule for a Large Number of Sources), is evaluated on synthetic mass functions. The experimental results verify that the rule can be effectively used to combine a large number of mass functions and to elicit the major opinion.

We present an adaptive approach to the construction of Gaussian process surrogates for Bayesian inference with expensive-to-evaluate forward models. Our method relies on the fully Bayesian approach to training Gaussian process models and utilizes the expected improvement idea from Bayesian global optimization. We adaptively construct training designs by maximizing the expected improvement in fit of the Gaussian process model to the noisy observational data. Numerical experiments on model problems with synthetic data demonstrate the effectiveness of the obtained adaptive designs compared to the fixed non-adaptive designs in terms of accurate posterior estimation at a fraction of the cost of inference with forward models.

The accuracy of probability distributions inferred using machine-learning algorithms heavily depends on data availability and quality. In practical applications it is therefore fundamental to investigate the robustness of a statistical model to misspecification of some of its underlying probabilities. In the context of graphical models, investigations of robustness fall under the notion of sensitivity analyses. These analyses consist in varying some of the model's probabilities or parameters and then assessing how far apart the original and the varied distributions are. However, for Gaussian graphical models, such variations usually make the original graph an incoherent representation of the model's conditional independence structure. Here we develop an approach to sensitivity analysis which guarantees the original graph remains valid after any probability variation and we quantify the effect of such variations using different measures. To achieve this we take advantage of algebraic techniques to both concisely represent conditional independence and to provide a straightforward way of checking the validity of such relationships. Our methods are demonstrated to be robust and comparable to standard ones, which break the conditional independence structure of the model, using an artificial example and a medical real-world application.

We propose a general framework for solving statistical mechanics of systems with a finite size. The approach extends the celebrated variational mean-field approaches using autoregressive neural networks which support direct sampling and exact calculation of normalized probability of configurations. The network computes variational free energy, estimates physical quantities such as entropy, magnetizations and correlations, and generates uncorrelated samples all at once. Training of the network employs the policy gradient approach in reinforcement learning, which unbiasedly estimates the gradient of variational parameters. We apply our approach to several classical systems, including 2-d Ising models, Hopfield model, Sherrington--Kirkpatrick spin glasses, and the inverse Ising model, for demonstrating its advantages over existing variational mean-field methods. Our approach sheds light on solving statistical physics problems using modern deep generative neural networks.