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.

We consider Markov logic networks and relational logistic regression as two fundamental representation formalisms in statistical relational artificial intelligence that use weighted formulas in their specification. However, Markov logic networks are based on undirected graphs, while relational logistic regression is based on directed acyclic graphs. We show that when scaling the weight parameters with the domain size, the asymptotic behaviour of a relational logistic regression model is transparently controlled by the parameters, and we supply an algorithm to compute asymptotic probabilities. We also show using two examples that this is not true for Markov logic networks. We also discuss using several examples, mainly from the literature, how the application context can help the user to decide when such scaling is appropriate and when using the raw unscaled parameters might be preferable. We highlight random sampling as a particularly promising area of application for scaled models and expound possible avenues for further research.

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.

Natural language processing (NLP) and deep learning are growing in popularity for their use in ML technologies like self-driving cars and speech recognition software. As more companies begin to implement deep learning components and other machine learning practices, the demand for software developers and data scientists with proficiency in deep learning is skyrocketing. Today, we will introduce you to a popular deep learning project, the Text Generator, to familiarize you with important, industry-standard NLP concepts, including Markov chains. By the end of this article, you'll understand how to build a Text Generator component for search engine systems and the know-how to implement Markov chains for faster predictive models. Text generation is popular across the board and in every industry, especially for the mobile, app, and data science.

We present a formal language for specifying qualitative preferences over temporal goals and a preference-based planning method in stochastic systems. Using automata-theoretic modeling, the proposed specification allows us to express preferences over different sets of outcomes, where each outcome describes a set of temporal sequences of subgoals. We define the value of preference satisfaction given a stochastic process over possible outcomes and develop an algorithm for time-constrained probabilistic planning in labeled Markov decision processes where an agent aims to maximally satisfy its preference formula within a pre-defined finite time duration. We present experimental results using a stochastic gridworld example and discuss possible extensions of the proposed preference model.

Short text is a popular avenue of sharing feedback, opinions and reviews on social media, e-commerce platforms, etc. Many companies need to extract meaningful information (which may include thematic content as well as semantic polarity) out of such short texts to understand users' behaviour. However, obtaining high quality sentiment-associated and human interpretable themes still remains a challenge for short texts. In this paper we develop ELJST, an embedding enhanced generative joint sentiment-topic model that can discover more coherent and diverse topics from short texts. It uses Markov Random Field Regularizer that can be seen as a generalisation of skip-gram based models. Further, it can leverage higher-order semantic information appearing in word embedding, such as self-attention weights in graphical models. Our results show an average improvement of 10% in topic coherence and 5% in topic diversification over baselines. Finally, ELJST helps understand users' behaviour at more granular levels which can be explained. All these can bring significant values to the service and healthcare industries often dealing with customers.

We need to decide what proportion of salmons to catch in a year in a specific area maximizing the longer term return. Each salmon generates a fixed amount of dollar. But if a large proportion of salmons are caught then the yield of the next year will be lower. We need to find the optimum portion of salmons to catch to maximize the return over a long time period. Here we consider a simplified version of the above problem; whether to fish a certain portion of salmon or not.

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.