Probabilistic World Research Articles

World model learning and inference

Understanding information processing in the brain—and creating general-purpose artificial intelligence—are long-standing aspirations of scientists and engineers worldwide. The distinctive features of human intelligence are high-level cognition and control in various interactions with the world including the self, which are not defined in advance and are vary over time. The challenge of building human-like intelligent machines, as well as progress in brain science and behavioural analyses, robotics, and their associated theoretical formalisations, speaks to the importance of the world-model learning and inference. In this article, after briefly surveying the history and challenges of internal model learning and probabilistic learning, we introduce the free energy principle, which provides a useful framework within which to consider neuronal computation and probabilistic world models. Next, we showcase examples of human behaviour and cognition explained under that principle. We then describe symbol emergence in the context of probabilistic modelling, as a topic at the frontiers of cognitive robotics. Lastly, we review recent progress in creating human-like intelligence by using novel probabilistic programming languages. The striking consensus that emerges from these studies is that probabilistic descriptions of learning and inference are powerful and effective ways to create human-like artificial intelligent machines and to understand intelligence in the context of how humans interact with their world.

The Birthday Problem and Zero-Error List Codes

A key result of classical information theory states that if the rate of a randomly generated codebook is less than the mutual information between the channel's input and output, then the probability that that codebook has negligible error goes to one as the blocklength goes to infinity. In an attempt to bridge the gap between the probabilistic world of classical information theory and the combinatorial world of zero-error information theory, this work derives necessary and sufficient conditions on the rate so that the probability that a randomly generated codebook operated under list decoding (for any fixed list size) has zero error probability goes to one as the blocklength goes to infinity. Furthermore, this work extends the classical birthday problem to an information-theoretic setting, which results in the definition of a “noisy” counterpart of Rényi entropy, analogous to how mutual information can be considered a noisy counterpart of Shannon entropy.

Context-aware 3D object anchoring for mobile robots

A world model representing the elements in a robot’s environment needs to maintain a correspondence between the objects being observed and their internal representations, which is known as the anchoring problem. Anchoring is a key aspect for an intelligent robot operation, since it enables high-level functions such as task planning and execution. This work presents an anchoring system that continually integrates new observations from a 3D object recognition algorithm into a probabilistic world model. Our system takes advantage of the contextual relations inherent to human-made spaces in order to improve the classification results of the baseline object recognition system. To achieve that, the system builds a graph-based world model containing the objects in the scene (both in the current and previously perceived observations), which is exploited by a Probabilistic Graphical Model (PGM) in order to leverage contextual information during recognition. The world model also enables the system to exploit information about objects beyond the current field of view of the robot sensors. Most importantly, this is done in an online fashion, overcoming both the disadvantages of single-shot recognition systems (e.g., limited sensor aperture) and offline recognition systems that require prior registration of all frames of a scene (e.g., dynamic scenes, unsuitability for plan-based robot control). We also propose a novel way to include the outcome of local object recognition methods in the PGM, which results in a decrease in the usually high model learning complexity and an increase in the system performance. The system performance has been assessed with a dataset collected by a mobile robot from restaurant-like settings, obtaining positive results for both its data association and object recognition capabilities. The system has been successfully used in the RACE robotic architecture.

Membership testing for Bernoulli and tail-dependence matrices

Testing a given matrix for membership in the family of Bernoulli matrices is a long-standing problem; the many applications of Bernoulli vectors in computer science, finance, medicine, and operations research emphasize its practical relevance. After the three-variate case was covered by Chaganty and Joe (2006) by means of partial correlations, a novel approach towards this problem was taken by Fiebig et al. (2017) for low-dimensional settings, i.e., d≤6. The latter authors were the first to exploit the close relationship between the probabilistic world of Bernoulli matrices and the well-studied correlation and cut polytopes. Inspired by this approach, we use results from Deza and Laurent (1997), Embrechts et al. (2016), and Fiebig et al. (2017) in a pre-phase of a novel algorithm to check necessary as well as sufficient conditions, before actually testing a matrix for Bernoulli compatibility. In our main approach, however, we build upon an early attempt by Lee (1993) based on the vertex representation of the correlation polytope and directly solve the corresponding linear program. To deal appropriately with the issue of exponentially many primal variables, we propose a specifically tailored column generation method. A straightforward, yet novel, analysis of the arising subproblem of determining the most violated dual constraint in the column generation process leads to an exact algorithm for membership testing. Although the membership problem is known to be NP-complete, we observe very promising performance up to dimension d=40 on a broad variety of test problems. An important byproduct of the numerical solution is a representation for Bernoulli matrices with (only) d2 many vertices that gives rise to an efficient simulation routine.

A Feynman–Kac–Itô formula for magnetic Schrödinger operators on graphs

In this paper we prove a Feynman–Kac–Ito formula for magnetic Schrodinger operators on arbitrary weighted graphs. To do so, we have to provide a natural and general framework both on the operator theoretic and the probabilistic side of the equation. On the operator side we identify a very general class of potentials that allows the definition of magnetic Schrodinger operators. On the probabilistic side, we introduce an appropriate notion of stochastic line integrals with respect to magnetic potentials. Apart from linking the world of discrete magnetic operators with the probabilistic world through the Feynman–Kac–Ito formula, the insights from this paper gained on both sides should be of an independent interest. As applications of the Feynman–Kac–Ito formula, we prove a Kato inequality, a Golden–Thompson inequality and an explicit representation of the quadratic form domains corresponding to a large class of potentials.

Continuous creation in the probabilistic world of the theology of Chance

The aim of the paper is to present and analyze the doctrine of continuous creation typical for theism. Continuous creation is conceived of as divine causal action consisting in God’s bringing about the existence of any being at every moment of its existence. Such a definition of divine action, as N. Malebranche argued, leads to occasionalism – that is, to the view that God is the only cause in the world. In the first part of the paper, an attempt is made to demonstrate that Malebranche’s conclusion is valid and that two alternative views, weak and strong concurrentism, are not tenable. In the second part of the article, the idea of continuous creation is discussed, which can be formulated from the point of view of probabilistic theism.

God's Dice: The Law in a Probabilistic World

Despite the findings of natural scientists and philosophers, the law is still clinging on a deterministic concept of causation. Probabilistic considerations are not alien to the legal world, yet they are generally regarded as ad hoc exceptions to handle particularly complex cases. From this perspective, the need for a theoretical shift is advocated. Probabilistic causation should become the norm, whereas deterministic causation should only be used as a heuristic tool when confronted with prima facie deterministic cases. A distinction is drawn between the ex-ante and the ex-post probabilistic approach to causation. The former seems to be a better approach for lagged torts, whereas the latter is more appropriate to handle instant torts.

Domination in the Probabilistic World

In a probabilistic database, deciding if a tuple u is better than another tuple v has not a univocal solution, rather it depends on the specific Probabilistic Ranking Semantics (PRS) one wants to adopt so as to combine together tuples' scores and probabilities. In deterministic databases it is known that skyline queries are a remarkable alternative to (top- k ) ranking queries, because they remove from the user the burden of specifying a scoring function that combines values of different attributes into a single score. The skyline of a deterministic relation R is the set of undominated tuples in R -- tuple u dominates tuple v iff on all the attributes of interest u is better than or equal to v and strictly better on at least one attribute. Domination is equivalent to having s ( u ) ≥ s ( v ) for all monotone scoring functions s (). The skyline of a probabilistic relation R p can be similarly defined as the set of P-undominated tuples in R p , where now u P-dominates v iff, whatever monotone scoring function one would use to combine the skyline attributes, u is reputed better than v by the PRS at hand. This definition, which is applicable to arbitrary ranking semantics and probabilistic correlation models, is parametric in the adopted PRS, thus it ensures that ranking and skyline queries will always return consistent results. In this article we provide an overall view of the problem of computing the skyline of a probabilistic relation. We show how, under mild conditions that indeed hold for all known PRSs, checking P-domination can be cast into an optimization problem, whose complexity we characterize for a variety of combinations of ranking semantics and correlation models. For each analyzed case we also provide specific P-domination rules , which are exploited by the algorithm we detail for the case where the probabilistic model is known to the query processor. We also consider the case in which the probability of tuple events can only be obtained through an oracle, and describe another skyline algorithm for this loosely integrated scenario. Our experimental evaluation of P-domination rules and skyline algorithms confirms the theoretical analysis.

Entanglement and Quantum non-locality: an experimental perspective

The theory of Quantum Mechanics is one of the mainstay of modern physics, a well-established mathematical clockwork whose strength and accuracy in predictions are currently experienced in worldwide research laboratories. As a matter of fact, Quantum Mechanics laid the groundwork of a rich variety of studies ranging from solid state physics to cosmology, from bio-physics to particle physics. The up-to-date ability of manipulating single quantum states is paving the way for emergent quantum technologies as quantum information and computation, quantum communication, quantum metrology and quantum imaging. In spite of the impressive matemathical capacity, a long-standing debate is even revolving around the foundational axioms of this theory, the main bones of content being the non-local effects of entangled states, the wave function collapse and the concept of measurement in Quantum Mechanics, the macro-objectivation problem (the transition from a microscopic probabilistic world to a macroscopic deterministic world described by classical mechanics). Problems that, beyond their fundamental interest in basic science, now also concern the impact of these developing technologies. Without claiming to be complete, this article provides in outline the living matter concerning some of these problems, the implications of which extend deeply on the connection between entanglement and space-time structure.

Applying the Teachings of Behavioural Finance to Risk Arbitrage Strategy

Contrary to classic financial strategy based on the rational behaviour of economic agents, behavioural finance offers a more pragmatic vision of markets, notably by applying psychology.It is now fairly widely acknowledged that the assumption of market efficiency upon which classic financial strategy is based is not a good way to explain the operation of capital markets. Conversely, behavioural finance is able to furnish some very interesting answers by taking a fresh look at the decision-making process of investors. Many studies have thereby made the link between the forming of prices on equity markets and the behavioural biases of long only and long-short managers. Yet to our knowledge, there are no research papers that associate both behavioural finance and the alternative strategy of risk arbitrage.In this document, we therefore propose to apply the cognitive science approach to the study of this theory, which we have been using in our funds for more than 10 years. From the preparation of a M&A deal by a potential buyer to the establishment of the strategy in the portfolio by the arbitrageur, all the players on the chain are ideal subject matter for behavioural finance. Indeed, they share the same characteristic of having to make important decisions in an uncertain, probabilistic world that is saturated with information.To begin with, we present the general principles of behavioural finance by rounding up the scientific literature on the subject. In particular, we see how the main biases of financial market players are organised. We then go on to illustrate these biases with concrete examples drawn from the experience of our risk arbitrage management team. We conclude by showing that behavioural finance can be a precious tool in the management of a risk arbitrage portfolio.

Symbolic representation of probabilistic worlds

Symbolic representation of environmental variables is a ubiquitous and often debated component of cognitive science. Yet notwithstanding centuries of philosophical discussion, the efficacy, scope, and validity of such representation has rarely been given direct consideration from a mathematical point of view. This paper introduces a quantitative measure of the effectiveness of symbolic representation, and develops formal constraints under which such representation is in fact warranted. The effectiveness of symbolic representation hinges on the probabilistic structure of the environment that is to be represented. For arbitrary probability distributions (i.e., environments), symbolic representation is generally not warranted. But in modal environments, defined here as those that consist of mixtures of component distributions that are narrow (“spiky”) relative to their spreads, symbolic representation can be shown to represent the environment with a relatively negligible loss of information. Modal environments support propositional forms, logical relations, and other familiar features of symbolic representation. Hence the assumption that our environment is, in fact, modal is a key tacit assumption underlying the use of symbols in cognitive science.

Introduction: Thinking Possibilistically in a Probabilistic World

The papers in this section demonstrate several interesting points about disasters, and about academic interest in them, including a remarkable convergence of perspective about what is important: the extent and dimensions of peoples suffering as a result of disaster; the view that conventional approaches to thinking about disaster are insufficient; the realization that the idea of Anatural disaster misleadingly draws attention away from the pre-existing conditions that make people vulnerable to hazards in the first place. All agree, too, that at least two of the three of the big troika of inequalityCrace, class, and genderCare crucial. Notably absent at the conference from which these papers came was any deep discussion of gender; indeed, notably absent from the program were women. Their absence was not because of lack of effort on the part of the conference organizers to invite female scholars. Female scholars were invited, but could not attend. Their absence is evidence of a paucity of female scholars in the field.

The ultimate sampling dilemma in experience-based decision making.

Computer simulations and 2 experiments demonstrate the ultimate sampling dilemma, which constitutes a serious obstacle to inductive inferences in a probabilistic world. Participants were asked to take the role of a manager who is to make purchasing decisions based on positive versus negative feedback about 3 providers in 2 different product domains. When information sampling (from a computerized database) was over, they had to make inferences about actual differences in the database from which the sample was drawn (e.g., about the actual superiority of different providers, or about the most likely origins of negatively valenced products). The ultimate sampling dilemma consists in a forced choice between 2 search strategies that both have their advantages and their drawbacks: natural sampling and deliberate sampling of information relevant to the inference task. Both strategies leave the sample unbiased for specific inferences but create errors or biases for other inferences.

Challenging Greco-Roman Argumentation Trajectories: Argument Norms and Cultural Traditions

A common in western scholarship is that is to be valorized, generally, as a key component of decisions, and, specifically, as an essential tool for life in western, democratic societies. Klumpp, Hollihan, and Riley (2002) note study of practice has developed out of a sense of commitment to a democratic process of deliberation, organized and institutionalized debate, and then political action (p. 579). Zarefsky (2002) describes the pedagogic emphasis of the field as study and teaching of general argumentation, which in turn has been seen as valuable equipment for citizenship in a complex society (p. 35). Kauffeld (2002) suggests that, in our culture learning, institutions, public life, even the economy, all depend on argumentation (p. 24). Hence, scholars are generally secure in their belief that good practices are essential in both our personal and public lives in sorting out ideas and arriving at the best possible decision, given the situation. This commitment to is, in large part, a direct result of our European intellectual tradition. As Branham (1991) notes: basic assumption of Greek and Roman debate is widely held today--that wise decisions (whether in governance or the administration of justice) can only be reached through the clash of conflicting points of view (p. 8). Yet this inheritance is unique to the west, and consequently, our fascination with argument as the central component of decision-making processes may deserve to be interrogated. Indeed, Zarefsky (2002) calls for further comparative study of argumentation. He maintains that looking outside our culture will help us know better where our findings need to be relativized and where we may have insights that are valid across (p. 36). Comparative studies of in different cultures can bring to light literatures that have been overlooked or marginalized and promote new understandings of processes and practices. This issue of Argumentation and Advocacy begins with the that can be conceived and performed in a variety of ways. Argumentation is a manifestation of particular patterns of human interaction drawn from diverse assumptions regarding everything from the nature of reality to the most preferable ways for humans to live. In short, cultural patterns and traditions form an environmental field that conditions the precepts, principles, and trajectories of argumentation. This issue offers an exciting opportunity to feature scholar ship grounded in cultures that, in various ways, function outside of traditional Greco-Roman trajectories. The essays examine classical and contemporary perspectives drawn from Daoist philosophy, Hebraic faith, Native American practices, and Japanese traditions. They do not condemn Greco-Roman traditions of argument or suggest that any particular system is superior to another; rather, the essays help us understand the rich and complex nature of as a vital enterprise that is intimately connected to human experience. In the first essay, Useless/Usefulness of Argumentation: The Dao of Disputation, Steven Combs focuses on Daoism (Taoism), a key component of the Chinese philosophical tradition and many Asian cultures. The essay highlights key differences in Chinese and Greco-Roman ideas on cosmology, knowledge and reason, and language, in order to demonstrate the larger system of thought that collaborates in theories. Daoist privileges intuitive knowledge over reasoning and denounces the ability of language to reflect reality accurately. Ultimately, and unlike Greco-Roman practices, Daoist argument does not attempt to provide the best possible answers to questions posed in a probabilistic world, but rather embraces ambiguity and uncertainty in order to open up new possibilities for belief and action. …

A New Criterion for Comparing Fuzzy Logics for Uncertain Reasoning

A new criterion is introduced for judging the suitability of various “fuzzy logics” for practical uncertain reasoning in a probabilistic world and the relationship of this criterion to several established criteria, and its consequences for truth functional belief, are investigated.

Finding MAPs for belief networks is NP-hard

Given a probabilistic world model, an important problem is to find the maximum a-posteriori probability (MAP) instantiation of all the random variables given the evidence. Numerous researchers using such models employ some graph representation for the distributions, such as a Bayesian belief network. This representation simplifies the complexity of specifying the distributions from exponential in n, the number of variables in the model, to linear in n, in many interesting cases. We show, however, that finding the MAP is NP-hard in the general case when these representations are used, even if the size of the representation happens to be linear in n. Furthermore, minor modifications to the proof show that the problem remains NP-hard for various restrictions of the topology of the graphs. The same technique can be applied to the results of a related paper (by Cooper), to further restrict belief network topology in the proof that probabilistic inference is NP-hard.