Markov networks are popular models for discrete multivariate systems where the dependence structure of the variables is specified by an undirected graph. To allow for more expressive dependence structures, several generalizations of Markov networks have been proposed. Here we consider the class of contextual Markov networks which takes into account possible context-specific independences among pairs of variables. Structure learning of contextual Markov networks is very challenging due to the extremely large number of possible structures. One of the main challenges has been to design a score, by which a structure can be assessed in terms of model fit related to complexity, without assuming chordality. Here we introduce the marginal pseudo-likelihood as an analytically tractable criterion for general contextual Markov networks. Our criterion is shown to yield a consistent structure estimator. Experiments demonstrate the favorable properties of our method in terms of predictive accuracy of the inferred models.

A project-based course to build an AIoT system from theory to prototype. Artificial Intelligence and Automation with Zang Cloud Sample codes are provided for every project in this course. You will receive a certificate of completion when finishing this course. There is also Udemy 30 Day Money Back Guarantee, if you are not satisfied with this course. This course teaches you how to build an AIoT system from theory to prototype particularly using Naive Bayes algorithm.

Unobserved confounding is one of the greatest challenges for causal discovery. The case in which unobserved variables have a widespread effect on many of the observed ones is particularly difficult because most pairs of variables are conditionally dependent given any other subset, rendering the causal effect unidentifiable. In this paper we show that beyond conditional independencies, under the principle of independent mechanisms, unobserved confounding in this setting leaves a statistical footprint in the observed data distribution that allows for disentangling spurious and causal effects. Using this insight, we demonstrate that a sparse linear Gaussian directed acyclic graph among observed variables may be recovered approximately and propose an adjusted score-based causal discovery algorithm that may be implemented with general purpose solvers and scales to high-dimensional problems. We find, in addition, that despite the conditions we pose to guarantee causal recovery, performance in practice is robust to large deviations in model assumptions.

Trained AI systems and expert decision makers can make errors that are often difficult to identify and understand. Determining the root cause for these errors can improve future decisions. This work presents Generative Error Model (GEM), a generative model for inferring representational errors based on observations of an actor's behavior (either simulated agent, robot, or human). The model considers two sources of error: those that occur due to representational limitations -- "blind spots" -- and non-representational errors, such as those caused by noise in execution or systematic errors present in the actor's policy. Disambiguating these two error types allows for targeted refinement of the actor's policy (i.e., representational errors require perceptual augmentation, while other errors can be reduced through methods such as improved training or attention support). We present a Bayesian inference algorithm for GEM and evaluate its utility in recovering representational errors on multiple domains. Results show that our approach can recover blind spots of both reinforcement learning agents as well as human users.

Now, we're going to see how we can use our training data to train our Naive Bayes' model. What does it even mean to train a Naive Bayes' model? In our task, we have two classes. So, n 2. Let's work our way through this formula and see how these different terms are calculated. First, let's look at the P(c) term.

We study the problem of diffeomorphometric geodesic landmark matching where the objective is to find a diffeomorphism that via its group action maps between two sets of landmarks. It is well-known that the motion of the landmarks, and thereby the diffeomorphism, can be encoded by an initial momentum leading to a formulation where the landmark matching problem can be solved as an optimisation problem over such momenta. The novelty of our work lies in the application of a derivative-free Bayesian inverse method for learning the optimal momentum encoding the diffeomorphic mapping between the template and the target. The method we apply is the ensemble Kalman filter, an extension of the Kalman filter to nonlinear observation operators. We describe an efficient implementation of the algorithm and show several numerical results for various target shapes.

While Shapley Values (SV) are one of the gold standard for interpreting machine learning models, we show that they are still poorly understood, in particular in the presence of categorical variables or of variables of low importance. For instance, we show that the popular practice that consists in summing the SV of dummy variables is false as it provides wrong estimates of all the SV in the model and implies spurious interpretations. Based on the identification of null and active coalitions, and a coalitional version of the SV, we provide a correct computation and inference of important variables. Moreover, a Python library (All the experiments and simulations can be reproduced with the publicly available library Active Coalition of Variables, https://www.github.com/salimamoukou/acv00) that computes reliably conditional expectations and SV for tree-based models, is implemented and compared with state-of-the-art algorithms on toy models and real data sets.

Online algorithms for detecting changepoints, or abrupt shifts in the behavior of a time series, are often deployed with limited resources, e.g., to edge computing settings such as mobile phones or industrial sensors. In these scenarios it may be beneficial to trade the cost of collecting an environmental measurement against the quality or "fidelity" of this measurement and how the measurement affects changepoint estimation. For instance, one might decide between inertial measurements or GPS to determine changepoints for motion. A Bayesian approach to changepoint detection is particularly appealing because we can represent our posterior uncertainty about changepoints and make active, cost-sensitive decisions about data fidelity to reduce this posterior uncertainty. Moreover, the total cost could be dramatically lowered through active fidelity switching, while remaining robust to changes in data distribution. We propose a multi-fidelity approach that makes cost-sensitive decisions about which data fidelity to collect based on maximizing information gain with respect to changepoints. We evaluate this framework on synthetic, video, and audio data and show that this information-based approach results in accurate predictions while reducing total cost.

Causal induction, i.e., identifying unobservable mechanisms that lead to the observable relations among variables, has played a pivotal role in modern scientific discovery, especially in scenarios with only sparse and limited data. Humans, even young toddlers, can induce causal relationships surprisingly well in various settings despite its notorious difficulty. However, in contrast to the commonplace trait of human cognition is the lack of a diagnostic benchmark to measure causal induction for modern Artificial Intelligence (AI) systems. Therefore, in this work, we introduce the Abstract Causal REasoning (ACRE) dataset for systematic evaluation of current vision systems in causal induction. Motivated by the stream of research on causal discovery in Blicket experiments, we query a visual reasoning system with the following four types of questions in either an independent scenario or an interventional scenario: direct, indirect, screening-off, and backward-blocking, intentionally going beyond the simple strategy of inducing causal relationships by covariation. By analyzing visual reasoning architectures on this testbed, we notice that pure neural models tend towards an associative strategy under their chance-level performance, whereas neuro-symbolic combinations struggle in backward-blocking reasoning. These deficiencies call for future research in models with a more comprehensive capability of causal induction.

We consider a sequential assortment selection problem where the user choice is given by a multinomial logit (MNL) choice model whose parameters are unknown. In each period, the learning agent observes a $d$-dimensional contextual information about the user and the $N$ available items, and offers an assortment of size $K$ to the user, and observes the bandit feedback of the item chosen from the assortment. We propose upper confidence bound based algorithms for this MNL contextual bandit. The first algorithm is a simple and practical method which achieves an $\tilde{\mathcal{O}}(d\sqrt{T})$ regret over $T$ rounds. Next, we propose a second algorithm which achieves a $\tilde{\mathcal{O}}(\sqrt{dT})$ regret. This matches the lower bound for the MNL bandit problem, up to logarithmic terms, and improves on the best known result by a $\sqrt{d}$ factor. To establish this sharper regret bound, we present a non-asymptotic confidence bound for the maximum likelihood estimator of the MNL model that may be of independent interest as its own theoretical contribution. We then revisit the simpler, significantly more practical, first algorithm and show that a simple variant of the algorithm achieves the optimal regret for a broad class of important applications.