In this article we present the motivation and the core thesis towards the implementation of a Quantum Knowledge Seeking Agent (QKSA). QKSA is a general reinforcement learning agent that can be used to model classical and quantum dynamics. It merges ideas from universal artificial general intelligence, constructor theory and genetic programming to build a robust and general framework for testing the capabilities of the agent in a variety of environments. It takes the artificial life (or, animat) path to artificial general intelligence where a population of intelligent agents are instantiated to explore valid ways of modelling the perceptions. The multiplicity and survivability of the agents are defined by the fitness, with respect to the explainability and predictability, of a resource-bounded computational model of the environment. This general learning approach is then employed to model the physics of an environment based on subjective observer states of the agents. A specific case of quantum process tomography as a general modelling principle is presented. The various background ideas and a baseline formalism are discussed in this article which sets the groundwork for the implementations of the QKSA that are currently in active development.

The performance of state-of-the-art baselines in the offline RL regime varies widely over the spectrum of dataset qualities, ranging from "far-from-optimal" random data to "close-to-optimal" expert demonstrations. We re-implement these under a fair, unified, and highly factorized framework, and show that when a given baseline outperforms its competing counterparts on one end of the spectrum, it never does on the other end. This consistent trend prevents us from naming a victor that outperforms the rest across the board. We attribute the asymmetry in performance between the two ends of the quality spectrum to the amount of inductive bias injected into the agent to entice it to posit that the behavior underlying the offline dataset is optimal for the task. The more bias is injected, the higher the agent performs, provided the dataset is close-to-optimal. Otherwise, its effect is brutally detrimental. Adopting an advantage-weighted regression template as base, we conduct an investigation which corroborates that injections of such optimality inductive bias, when not done parsimoniously, makes the agent subpar in the datasets it was dominant as soon as the offline policy is sub-optimal. In an effort to design methods that perform well across the whole spectrum, we revisit the generalized policy iteration scheme for the offline regime, and study the impact of nine distinct newly-introduced proposal distributions over actions, involved in proposed generalization of the policy evaluation and policy improvement update rules. We show that certain orchestrations strike the right balance and can improve the performance on one end of the spectrum without harming it on the other end.

Learning the structure of Bayesian networks and causal relationships from observations is a common goal in several areas of science and technology. We show that the prequential minimum description length principle (MDL) can be used to derive a practical scoring function for Bayesian networks when flexible and overparametrized neural networks are used to model the conditional probability distributions between observed variables. MDL represents an embodiment of Occam's Razor and we obtain plausible and parsimonious graph structures without relying on sparsity inducing priors or other regularizers which must be tuned. Empirically we demonstrate competitive results on synthetic and real-world data. The score often recovers the correct structure even in the presence of strongly nonlinear relationships between variables; a scenario were prior approaches struggle and usually fail. Furthermore we discuss how the the prequential score relates to recent work that infers causal structure from the speed of adaptation when the observations come from a source undergoing distributional shift.

When machine learning systems meet real world applications, accuracy is only one of several requirements. In this paper, we assay a complementary perspective originating from the increasing availability of pre-trained and regularly improving state-of-the-art models. While new improved models develop at a fast pace, downstream tasks vary more slowly or stay constant. Assume that we have a large unlabelled data set for which we want to maintain accurate predictions. Whenever a new and presumably better ML models becomes available, we encounter two problems: (i) given a limited budget, which data points should be re-evaluated using the new model?; and (ii) if the new predictions differ from the current ones, should we update? Problem (i) is about compute cost, which matters for very large data sets and models. Problem (ii) is about maintaining consistency of the predictions, which can be highly relevant for downstream applications; our demand is to avoid negative flips, i.e., changing correct to incorrect predictions. In this paper, we formalize the Prediction Update Problem and present an efficient probabilistic approach as answer to the above questions. In extensive experiments on standard classification benchmark data sets, we show that our method outperforms alternative strategies along key metrics for backward-compatible prediction updates.

When a population exhibits heterogeneity, we often model it via a finite mixture: decompose it into several different but homogeneous subpopulations. Contemporary practice favors learning the mixtures by maximizing the likelihood for statistical efficiency and the convenient EM-algorithm for numerical computation. Yet the maximum likelihood estimate (MLE) is not well defined for the most widely used finite normal mixture in particular and for finite location-scale mixture in general. We hence investigate feasible alternatives to MLE such as minimum distance estimators. Recently, the Wasserstein distance has drawn increased attention in the machine learning community. It has intuitive geometric interpretation and is successfully employed in many new applications. Do we gain anything by learning finite location-scale mixtures via a minimum Wasserstein distance estimator (MWDE)? This paper investigates this possibility in several respects. We find that the MWDE is consistent and derive a numerical solution under finite location-scale mixtures. We study its robustness against outliers and mild model mis-specifications. Our moderate scaled simulation study shows the MWDE suffers some efficiency loss against a penalized version of MLE in general without noticeable gain in robustness. We reaffirm the general superiority of the likelihood based learning strategies even for the non-regular finite location-scale mixtures.

Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural simulator-based inference algorithm which simultaneously offers simulation efficiency and fast empirical posterior testability, which is unique among modern algorithms. Our approach is simulation efficient by simultaneously estimating low-dimensional marginal posteriors instead of the joint posterior and by proposing simulations targeted to an observation of interest via a prior suitably truncated by an indicator function. Furthermore, by estimating a locally amortized posterior our algorithm enables efficient empirical tests of the robustness of the inference results. Such tests are important for sanity-checking inference in real-world applications, which do not feature a known ground truth. We perform experiments on a marginalized version of the simulation-based inference benchmark and two complex and narrow posteriors, highlighting the simulator efficiency of our algorithm as well as the quality of the estimated marginal posteriors. Implementation on GitHub.

Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph, and each node has a conditional probability table. Learning and inference are realized locally on individual nodes; therefore, computation remains tractable even with a large number of variables. However, the dependency network's learned distribution is the stationary distribution of a Markov chain called pseudo-Gibbs sampling and has no closed-form expressions. This technical disadvantage has impeded the development of dependency networks. In this paper, we consider a certain manifold for each node. Then, we can interpret pseudo-Gibbs sampling as iterative m-projections onto these manifolds. This interpretation provides a theoretical bound for the location where the stationary distribution of pseudo-Gibbs sampling exists in distribution space. Furthermore, this interpretation involves structure and parameter learning algorithms as optimization problems. In addition, we compare dependency and Bayesian networks experimentally. The results demonstrate that the dependency network and the Bayesian network have roughly the same performance in terms of the accuracy of their learned distributions. The results also show that the dependency network can learn much faster than the Bayesian network.

Since then, it has been of interest both for theoretical researcher and application scientists for applications varying from financial analysis, text summarization, image processing, information retrieval, stock prediction to keyword extraction, feature selection to mention a few. Fuzzy Rough Set (Pawlak, 1982, Jensen and Shen, 2004) was proposed for fuzzification of lower and upper approximation, which in applications to problems is very intuitive and useful, given the fact that each member of the universe bears a membership to the set under consideration. Since, there are two sets in a Rough Set based application namely lower approximation and upper approximation, hence, there are two Fuzzy Sets under study in the domains of Fuzzy Rough Set based analysis. In problems in which two Fuzzy Rough Sets have been computed and compared, how to determine the similarity and other relations between these pairs of Fuzzy Rough Sets? This can be illustrated with the example of application validated in this paper, viz.

Many common machine learning methods involve the geometric annealing path, a sequence of intermediate densities between two distributions of interest constructed using the geometric average. While alternatives such as the moment-averaging path have demonstrated performance gains in some settings, their practical applicability remains limited by exponential family endpoint assumptions and a lack of closed form energy function. In this work, we introduce $q$-paths, a family of paths which is derived from a generalized notion of the mean, includes the geometric and arithmetic mixtures as special cases, and admits a simple closed form involving the deformed logarithm function from nonextensive thermodynamics. Following previous analysis of the geometric path, we interpret our $q$-paths as corresponding to a $q$-exponential family of distributions, and provide a variational representation of intermediate densities as minimizing a mixture of $\alpha$-divergences to the endpoints. We show that small deviations away from the geometric path yield empirical gains for Bayesian inference using Sequential Monte Carlo and generative model evaluation using Annealed Importance Sampling.

Over the last few decades, various methods have been proposed for estimating prediction intervals in regression settings, including Bayesian methods, ensemble methods, direct interval estimation methods and conformal prediction methods. An important issue is the calibration of these methods: the generated prediction intervals should have a predefined coverage level, without being overly conservative. In this work, we review the above four classes of methods from a conceptual and experimental point of view. Results on benchmark data sets from various domains highlight large fluctuations in performance from one data set to another. These observations can be attributed to the violation of certain assumptions that are inherent to some classes of methods. We illustrate how conformal prediction can be used as a general calibration procedure for methods that deliver poor results without a calibration step.