λPSI: exact inference for higher-order probabilistic programs

Weighted model counting and integration (WMC/WMI) are natural problems to which we can reduce many probabilistic inference tasks, e.g., in Bayesian networks, Markov networks, and probabilistic programs. Typically, we are given a first-order formula, where each satisfying assignment is associated with a weight---e.g., a probability of occurrence---and our goal is to compute the total weight of the formula. In this paper, we target exact inference techniques for WMI that leverage the power of satisfiability modulo theories (SMT) solvers to decompose a first-order formula in linear real arithmetic into a set of hyperrectangular regions whose weight is easy to compute. We demonstrate the challenges of hyperrectangular decomposition and present a novel technique that utilizes orthogonal transformations to transform formulas in order to enable efficient inference. Our evaluation demonstrates our technique's ability to improve the time required to achieve exact probability bounds.

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Scaling exact inference for discrete probabilistic programs

Proceedings of the ACM on Programming Languages ◽

10.1145/3428208 ◽

2020 ◽

Vol 4 (OOPSLA) ◽

pp. 1-31

Author(s):

Steven Holtzen ◽

Guy Van den Broeck ◽

Todd Millstein

Keyword(s):

Exact Inference ◽

Probabilistic Programs

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Bayesian strategies: probabilistic programs as generalised graphical models

Programming Languages and Systems - Lecture Notes in Computer Science ◽

10.1007/978-3-030-72019-3_19 ◽

2021 ◽

pp. 519-547

Author(s):

Hugo Paquet

Keyword(s):

Bayesian Networks ◽

Graphical Models ◽

Graphical Representation ◽

Denotational Semantics ◽

Higher Order ◽

Control Flow ◽

Game Semantics ◽

Conditional Statements ◽

New Interpretation ◽

Probabilistic Programs

AbstractWe introduceBayesian strategies, a new interpretation of probabilistic programs in game semantics. This interpretation can be seen as a refinement of Bayesian networks.Bayesian strategies are based on a new form ofevent structure, with two causal dependency relations respectively modelling control flow and data flow. This gives a graphical representation for probabilistic programs which resembles the concrete representations used in modern implementations of probabilistic programming.From a theoretical viewpoint, Bayesian strategies provide a rich setting for denotational semantics. To demonstrate this we give a model for a general higher-order programming language with recursion, conditional statements, and primitives for sampling from continuous distributions and trace re-weighting. This is significant because Bayesian networks do not easily support higher-order functions or conditionals.

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Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

Behavioral and Brain Sciences ◽

10.1017/s0140525x19000451 ◽

2019 ◽

Vol 42 ◽

Author(s):

Daniel J. Povinelli ◽

Gabrielle C. Glorioso ◽

Shannon L. Kuznar ◽

Mateja Pavlic

Keyword(s):

Temporal Reasoning ◽

Higher Order ◽

Important Case ◽

Human Cognition ◽

Relational Reasoning ◽

Dual Systems ◽

First Order ◽

Reasoning System ◽

Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

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Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100132741 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1622-1623

Author(s):

G.F. Bastin ◽

H.J.M. Heijligers

Keyword(s):

Background Subtraction ◽

Electron Probe ◽

Detection System ◽

Higher Order ◽

Light Elements ◽

Strong Suppression ◽

Electron Probe Microanalyzer ◽

Quantitative Epma ◽

Peak Count ◽

Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

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Effects of Higher-Order Laue Zone reflections on structure images

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100148083 ◽

1993 ◽

Vol 51 ◽

pp. 450-451

Author(s):

H. S. Kim ◽

S. S. Sheinin

Keyword(s):

Wave Vector ◽

Theoretical Calculations ◽

Reciprocal Lattice ◽

Image Plane ◽

Bloch Wave ◽

Dynamical Theory ◽

Higher Order ◽

Lattice Image ◽

Lattice Vector ◽

Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

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