Causal effect identification considers whether an interventional probability distribution can be uniquely determined from a passively observed distribution in a given causal structure. If the generating system induces context-specific independence (CSI) relations, the existing identification procedures and criteria based on do-calculus are inherently incomplete. We show that deciding causal effect non-identifiability is NP-hard in the presence of CSIs. Motivated by this, we design a calculus and an automated search procedure for identifying causal effects in the presence of CSIs. The approach is provably sound and it includes standard do-calculus as a special case. With the approach we can obtain identifying formulas that were unobtainable previously, and demonstrate that a small number of CSI-relations may be sufficient to turn a previously non-identifiable instance to identifiable.

Making decisions freely presupposes that there is some indeterminacy in the environment and in the decision making engine. The former is reflected on the behavioral changes due to communicating: few changes indicate rigid environments; productive changes manifest a moderate indeterminacy, but a large communicating effort with few productive changes characterize a chaotic environment. Hence, communicating, effective decision making and productive behavioral changes are related. The entropy measures the indeterminacy of the environment, and there is an entropy range in which communicating supports effective decision making. This conjecture is referred to here as the The Potential Productivity of Decisions. The computing engine that is causal to decision making should also have some indeterminacy. However, computations performed by standard Turing Machines are predetermined. To overcome this limitation an entropic mode of computing that is called here Relational-Indeterminate is presented. Its implementation in a table format has been used to model an associative memory. The present theory and experiment suggest the Entropy Trade-off: There is an entropy range in which computing is effective but if the entropy is too low computations are too rigid and if it is too high computations are unfeasible. The entropy trade-off of computing engines corresponds to the potential productivity of decisions of the environment. The theory is referred to an Interaction-Oriented Cognitive Architecture. Memory, perception, action and thought involve a level of indeterminacy and decision making may be free in such degree. The overall theory supports an ecological view of rationality. The entropy of the brain has been measured in neuroscience studies and the present theory supports that the brain is an entropic machine. The paper is concluded with a number of predictions that may be tested empirically.

Predicting undesirable events during the execution of a business process instance provides the process participants with an opportunity to intervene and keep the process aligned with its goals. Few approaches for tackling this challenge consider a multi-perspective view, where the flow perspective of the process is combined with its surrounding context. Given the many sources of data in today's world, context can vary widely and have various meanings. This paper addresses the issue of context being cause or effect of the next event and its impact on next event prediction. We leverage previous work on probabilistic models to develop a Dynamic Bayesian Network technique. Probabilistic models are considered comprehensible and they allow the end-user and his or her understanding of the domain to be involved in the prediction. Our technique models context attributes that have either a cause or effect relationship towards the event. We evaluate our technique with two real-life data sets and benchmark it with other techniques from the field of predictive process monitoring. The results show that our solution achieves superior prediction results if context information is correctly introduced into the model.

We propose a general framework to robustly characterize joint and conditional probability distributions via transport maps. Transport maps or "flows" deterministically couple two distributions via an expressive monotone transformation. Yet, learning the parameters of such transformations in high dimensions is challenging given few samples from the unknown target distribution, and structural choices for these transformations can have a significant impact on performance. Here we formulate a systematic framework for representing and learning monotone maps, via invertible transformations of smooth functions, and demonstrate that the associated minimization problem has a unique global optimum. Given a hierarchical basis for the appropriate function space, we propose a sample-efficient adaptive algorithm that estimates a sparse approximation for the map. We demonstrate how this framework can learn densities with stable generalization performance across a wide range of sample sizes on real-world datasets.

We propose a generative Causal Adversarial Network (CAN) for learning and sampling from conditional and interventional distributions. In contrast to the existing CausalGAN which requires the causal graph to be given, our proposed framework learns the causal relations from the data and generates samples accordingly. The proposed CAN comprises a two-fold process namely Label Generation Network (LGN) and Conditional Image Generation Network (CIGN). The LGN is a GAN-based architecture which learns and samples from the causal model over labels. The sampled labels are then fed to CIGN, a conditional GAN architecture, which learns the relationships amongst labels and pixels and pixels themselves and generates samples based on them. This framework is equipped with an intervention mechanism which enables. the model to generate samples from interventional distributions. We quantitatively and qualitatively assess the performance of CAN and empirically show that our model is able to generate both interventional and conditional samples without having access to the causal graph for the application of face generation on CelebA data.

Most reinforcement learning methods are based upon the key assumption that the transition dynamics and reward functions are fixed, that is, the underlying Markov decision process is stationary. However, in many real-world applications, this assumption is violated, and using existing algorithms may result in a performance lag. To proactively search for a good future policy, we present a policy gradient algorithm that maximizes a forecast of future performance. This forecast is obtained by fitting a curve to the counter-factual estimates of policy performance over time, without explicitly modeling the underlying non-stationarity. The resulting algorithm amounts to a non-uniform reweighting of past data, and we observe that minimizing performance over some of the data from past episodes can be beneficial when searching for a policy that maximizes future performance. We show that our algorithm, called Prognosticator, is more robust to non-stationarity than two online adaptation techniques, on three simulated problems motivated by real-world applications.

Contact-tracing is an essential tool in order to mitigate the impact of pandemic such as the COVID-19. In order to achieve efficient and scalable contact-tracing in real time, digital devices can play an important role. While a lot of attention has been paid to analyzing the privacy and ethical risks of the associated mobile applications, so far much less research has been devoted to optimizing their performance and assessing their impact on the mitigation of the epidemic. We develop Bayesian inference methods to estimate the risk that an individual is infected. This inference is based on the list of his recent contacts and their own risk levels, as well as personal information such as results of tests or presence of syndromes. We propose to use probabilistic risk estimation in order to optimize testing and quarantining strategies for the control of an epidemic. Our results show that in some range of epidemic spreading (typically when the manual tracing of all contacts of infected people becomes practically impossible, but before the fraction of infected people reaches the scale where a lockdown becomes unavoidable), this inference of individuals at risk could be an efficient way to mitigate the epidemic. Our approaches translate into fully distributed algorithms that only require communication between individuals who have recently been in contact. Such communication may be encrypted and anonymized and thus compatible with privacy preserving standards. We conclude that probabilistic risk estimation is capable to enhance performance of digital contact tracing and should be considered in the currently developed mobile applications. Identifying, calling, testing, and if needed quarantining the recent contacts of an individual who has just been tested positive is the standard route for limiting the transmission of a highly contagious virus.

Computer Vision practitioners must thoroughly understand their model's performance, but conditional evaluation is complex and error-prone. In biometric verification, model performance over continuous covariates---real-number attributes of images that affect performance---is particularly challenging to study. We develop a generative model of the match and non-match score distributions over continuous covariates and perform inference with modern Bayesian methods. We use mixture models to capture arbitrary distributions and local basis functions to capture non-linear, multivariate trends. Three experiments demonstrate the accuracy and effectiveness of our approach. First, we study the relationship between age and face verification performance and find previous methods may overstate performance and confidence. Second, we study preprocessing for CNNs and find a highly non-linear, multivariate surface of model performance. Our method is accurate and data efficient when evaluated against previous synthetic methods. Third, we demonstrate the novel application of our method to pedestrian tracking and calculate variable thresholds and expected performance while controlling for multiple covariates.

Efficient feature selection from high-dimensional datasets is a very important challenge in many data-driven fields of science and engineering. We introduce a statistical mechanics inspired strategy that addresses the problem of sparse feature selection in the context of binary classification by leveraging a computational scheme known as expectation propagation (EP). The algorithm is used in order to train a continuous-weights perceptron learning a classification rule from a set of (possibly partly mislabeled) examples provided by a teacher perceptron with diluted continuous weights. We test the method in the Bayes optimal setting under a variety of conditions and compare it to other state-of-the-art algorithms based on message passing and on expectation maximization approximate inference schemes. Overall, our simulations show that EP is a robust and competitive algorithm in terms of variable selection properties, estimation accuracy and computationally complexity, especially when the student perceptron is trained from correlated patterns that prevent other iterative methods from converging. Furthermore, our numerical tests demonstrate that the algorithm is capable of learning online the unknown values of prior parameters, such as the dilution level of the weights of the teacher perceptron and the fraction of mislabeled examples, quite accurately. This is achieved by means of a simple maximum likelihood strategy that consists in minimizing the free energy associated with the EP algorithm.

Continual learning from streaming data sources becomes more and more popular due to the increasing number of online tools and systems. Dealing with dynamic and everlasting problems poses new challenges for which traditional batch-based offline algorithms turn out to be insufficient in terms of computational time and predictive performance. One of the most crucial limitations is that we cannot assume having access to a finite and complete data set - we always have to be ready for new data that may complement our model. This poses a critical problem of providing labels for potentially unbounded streams. In the real world, we are forced to deal with very strict budget limitations, therefore, we will most likely face the scarcity of annotated instances, which are essential in supervised learning. In our work, we emphasize this problem and propose a novel instance exploitation technique. We show that when: (i) data is characterized by temporary non-stationary concepts, and (ii) there are very few labels spanned across a long time horizon, it is actually better to risk overfitting and adapt models more aggressively by exploiting the only labeled instances we have, instead of sticking to a standard learning mode and suffering from severe underfitting. We present different strategies and configurations for our methods, as well as an ensemble algorithm that attempts to maintain a sweet spot between risky and normal adaptation. Finally, we conduct a complex in-depth comparative analysis of our methods, using state-of-the-art streaming algorithms relevant to the given problem.