We consider the maximum-a-posteriori inference problem in discrete graphical models and study solvers based on the dual block-coordinate ascent rule. We map all existing solvers in a single framework, allowing for a better understanding of their design principles. We theoretically show that some block-optimizing updates are sub-optimal and how to strictly improve them. On a wide range of problem instances of varying graph connectivity, we study the performance of existing solvers as well as new variants that can be obtained within the framework. As a result of this exploration we build a new state-of-the art solver, performing uniformly better on the whole range of test instances.

We study the Wasserstein natural gradient in parametric statistical models with continuous sample spaces. Our approach is to pull back the $L^2$-Wasserstein metric tensor in the probability density space to a parameter space, equipping the latter with a positive definite metric tensor, under which it becomes a Riemannian manifold, named the Wasserstein statistical manifold. In general, it is not a totally geodesic sub-manifold of the density space, and therefore its geodesics will differ from the Wasserstein geodesics, except for the well-known Gaussian distribution case, a fact which can also be validated under our framework. We use the sub-manifold geometry to derive a gradient flow and natural gradient descent method in the parameter space. When parametrized densities lie in $\bR$, the induced metric tensor establishes an explicit formula. In optimization problems, we observe that the natural gradient descent outperforms the standard gradient descent when the Wasserstein distance is the objective function. In such a case, we prove that the resulting algorithm behaves similarly to the Newton method in the asymptotic regime. The proof calculates the exact Hessian formula for the Wasserstein distance, which further motivates another preconditioner for the optimization process. To the end, we present examples to illustrate the effectiveness of the natural gradient in several parametric statistical models, including the Gaussian measure, Gaussian mixture, Gamma distribution, and Laplace distribution.

Data Science and Machine learning have been growing strong for the past decade. We argue that to make the most of this exciting field we should resist the temptation of assuming that forecasting can be reduced to brute-force data analytics. This owes to the fact that modelling, as we illustrate below, requires mastering the art of selecting relevant variables. More specifically, we investigate the subtle relation between "data and models" by focussing on the role played by algorithmic complexity, which contributed to making mathematically rigorous the long-standing idea that to understand empirical phenomena is to describe the rules which generate the data in terms which are "simpler" than the data itself. A key issue for the appraisal of the relation between algorithmic complexity and algorithmic learning is to do with a much needed clarification on the related but distinct concepts of compressibility, determinism and predictability. To this end we will illustrate that the evolution law of a chaotic system is compressibile, but a generic initial condition for it is not, making the time series generated by chaotic systems incompressible in general. Hence knowledge of the rules which govern an empirical phenomenon are not sufficient for predicting its outcomes. In turn this implies that there is more to understanding phenomena than learning -- even from data alone -- such rules. This can be achieved only in those cases when we are capable of "good modelling". Clearly, the very idea of algorithmic complexity rests on Turing's seminal analysis of computation. This motivates our remarks on this extremely telling example of analogy-based abstract modelling which is nonetheless heavily informed by empirical facts.

In this letter, we present a novel Gaussian Process Learning-based Probabilistic Optimal Power Flow (GP-POPF) for solving POPF under renewable and load uncertainties of arbitrary distribution. The proposed method relies on a non-parametric Bayesian inference-based uncertainty propagation approach, called Gaussian Process (GP). We also suggest a new type of sensitivity called Subspace-wise Sensitivity, using observations on the interpretability of GP-POPF hyperparameters. The simulation results on 14-bus and 30-bus systems show that the proposed method provides reasonably accurate solutions when compared with Monte-Carlo Simulations (MCS) solutions at different levels of uncertain renewable penetration as well as load uncertainties, while requiring much less number of samples and elapsed time.

Multi-Agent Reinforcement Learning (MARL) encompasses a powerful class of methodologies that have been applied in a wide range of fields. An effective way to further empower these methodologies is to develop libraries and tools that could expand their interpretability and explainability. In this work, we introduce MARLeME: a MARL model extraction library, designed to improve explainability of MARL systems by approximating them with symbolic models. Symbolic models offer a high degree of interpretability, well-defined properties, and verifiable behaviour. Consequently, they can be used to inspect and better understand the underlying MARL system and corresponding MARL agents, as well as to replace all/some of the agents that are particularly safety and security critical.

The exploration of geometrical patterns stimulates imagination and encourages abstract reasoning which is a distinctive feature of human intelligence. In cognitive science, Gestalt principles such as symmetry have often explained significant aspects of human perception. We present a computational technique for building artificial intelligence (AI) agents that use symmetry as the organizing principle for addressing Dehaene's test of geometric intelligence \cite{dehaene2006core}. The performance of our model is on par with extant AI models of problem solving on the Dehaene's test and seems correlated with some elements of human behavior on the same test.

In this paper, we introduce a novel methodology to efficiently construct a corpus for question answering over structured data. For this, we introduce an intermediate representation that is based on the logical query plan in a database called Operation Trees (OT). This representation allows us to invert the annotation process without losing flexibility in the types of queries that we generate. Furthermore, it allows for fine-grained alignment of query tokens to OT operations. In our method, we randomly generate OTs from a context-free grammar. Afterwards, annotators have to write the appropriate natural language question that is represented by the OT. Finally, the annotators assign the tokens to the OT operations. We apply the method to create a new corpus OTTA (Operation Trees and Token Assignment), a large semantic parsing corpus for evaluating natural language interfaces to databases. We compare OTTA to Spider and LC-QuaD 2.0 and show that our methodology more than triples the annotation speed while maintaining the complexity of the queries. Finally, we train a state-of-the-art semantic parsing model on our data and show that our corpus is a challenging dataset and that the token alignment can be leveraged to increase the performance significantly.

In this paper, we propose a multi-timescale replay (MTR) buffer for improving continual learning in RL agents faced with environments that are changing continuously over time at timescales that are unknown to the agent. The basic MTR buffer comprises a cascade of sub-buffers that accumulate experiences at different timescales, enabling the agent to improve the tradeoff between adaptation to new data and retention of old knowledge. We also combine the MTR framework with invariant risk minimization [Arjovsky et al., 2019] with the idea of encouraging the agent to learn a policy that is robust across the various environments it encounters over time. The MTR methods are evaluated in three different continual learning settings on two continuous control tasks and, in many cases, show improvement over the baselines.

The complexity of state-of-the-art modeling techniques for image classification impedes the ability to explain model predictions in an interpretable way. Existing explanation methods generally create importance rankings in terms of pixels or pixel groups. However, the resulting explanations lack an optimal size, do not consider feature dependence and are only related to one class. Counterfactual explanation methods are considered promising to explain complex model decisions, since they are associated with a high degree of human interpretability. In this paper, SEDC is introduced as a model-agnostic instance-level explanation method for image classification to obtain visual counterfactual explanations. For a given image, SEDC searches a small set of segments that, in case of removal, alters the classification. As image classification tasks are typically multiclass problems, SEDC-T is proposed as an alternative method that allows specifying a target counterfactual class. We compare SEDC(-T) with popular feature importance methods such as LRP, LIME and SHAP, and we describe how the mentioned importance ranking issues are addressed. Moreover, concrete examples and experiments illustrate the potential of our approach (1) to obtain trust and insight, and (2) to obtain input for model improvement by explaining misclassifications.

Steen's (2018) Hintikka set properties for Church's type theory based on primitive equality are reduced to the Hintikka set properties of Benzm\"uller, Brown and Kohlhase (2004) which are based on the logical connectives negation, disjunction and universal quantification.