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About 10,000 papers for “Inference”

Variational Inference for Logical Inference

Guy Emerson, Ann Copestake · Apollo (University of Cambridge) · 2017

Functional Distributional Semantics is a framework that aims to learn, from text, semantic representations which can be interpreted in terms of truth. Here we make two contributions to this framework. The first is to show how a type of logical inference can be performed by evaluating conditional probabilities. The second is to make these calculations tractable by means of a variational approximation. This approximation also enables faster convergence during training, allowing us to close the gap with state-of-the-art vector space models when evaluating on semantic similarity. We demonstrate promising performance on two tasks.

Cited by 8Open access

MATHEMATICAL INFERENCE AND LOGICAL INFERENCE

Yacin Hamami · The Review of Symbolic Logic · 2018

Abstract The deviation of mathematical proof —proof in mathematical practice—from the ideal of formal proof —proof in formal logic—has led many philosophers of mathematics to reconsider the commonly accepted view according to which the notion of formal proof provides an accurate descriptive account of mathematical proof. This, in turn, has motivated a search for alternative accounts of mathematical proof purporting to be more faithful to the reality of mathematical practice. Yet, in order to develop and evaluate such alternative accounts, it appears as a necessary prerequisite to first possess a clear picture of what the deviation of mathematical proof from formal proof consists in. The present work aims to contribute building such a picture by investigating the relation between the elementary steps of deduction constituting the two types of proofs— mathematical inference and logical inference . Many claims have been made in the literature regarding the relation between mathematical inference and logical inference, most of them stating that the former is lacking properties that are constitutive of the latter. Such differentiating claims are, however, usually put forward without a clear conception of the properties occurring in them, and are generally considered to be immediately justified by our direct acquaintance, or phenomenological experience, with the two types of inferences. The present study purports to advance our understanding of the relation between mathematical inference and logical inference by developing a detailed philosophical analysis of the differentiating claims, that is, an analysis of the meaning of the differentiating claims—through the properties that occur in them—as well as the reasons that support them. To this end, we provide at the outset a representative list of the different properties of logical inference that have occurred in the differentiating claims, and we notice that they all boil down to the three properties of formality , generality , and mechanicality . For each one of these properties, our analysis proceeds in two steps: we first provide precise conceptual characterizations of the different ways logical inference has been said to be formal, general, and mechanical, in the philosophical and logical literature on formal proof; we then examine why mathematical inference does not appear to be formal, general, and mechanical, for the different variations of these notions identified. Our study results in a precise conceptual apparatus for expressing and discussing the properties differentiating mathematical inference from logical inference, and provides a first inventory of the various reasons supporting the observations of those differences. The differentiating claims constitute thus a set of data that any philosophical account of mathematical inference and proof purporting to be more faithful to mathematical practice ought to be able to accommodate and explain.

Cited by 10

Inference

National Cancer Institute · Definitions · 2020

Ope n Pe e r v ie w on Qe

Cited by 0Open access

Inference

Paul Schrimpf, Paul Schrimpf, Paul Schrimpf et al. · 2015

Cited by 0

Inference

Steve Y Oudot, Donald R. Sheehy, Steve Y Oudot et al. · 2013

Abstract: For points sampled near a compact set X, the persistence barcode of the Rips filtration built from the sample contains information about the homology of X as long as X satisfies some geometric assumptions. The Rips filtration is prohibitively large, however zigzag persistence can be used to keep the size linear. We present several species of Rips-like zigzags and compare them with respect to the signal-to-noise ratio, a measure of how well the underlying homology is represented in the persistence barcode relative to the noise in the barcode at the relevant scales. Some of these Rips-like zigzags have been available as part of the Dionysus library for several years while others are new. Interestingly, we show that some species of Rips zigzags will exhibit less noise than the (non-zigzag) Rips filtration itself. Thus, the Rips zigzag can offer improvements in both size complexity and signal-to-noise ratio. Along the way, we develop new techniques for manipulating and comparing persistence barcodes from zigzag modules. We give methods for reversing arrows and removing spaces from a zigzag. We also discuss factoring zigzags and a kind of interleaving of two zigzags that allows their barcodes to be compared. These techniques were developed to provide our theoretical analysis of the signalto-noise ratio of Rips-like zigzags, but they are of independent interest as they apply to zigzag modules generally. Key-words: Zigzag persistence, homology inference, Rips filtrations, applied topology

Cited by 0

Inference

Møller, Jesper; id_orcid 0000-0002-0008-6890 · VBN Forskningsportal (Aalborg Universitet) · 2010

Chapter 9: This contribution concerns statistical inference for parametric models used in stochastic geometry and based on quick and simple simulation free procedures as well as more comprehensive methods based on a maximum likelihood or Bayesian approach combined with markov chain Monte Carlo (MCMC) techniques. Due to space limitations the focus is on spatial point processes.

Cited by 0

Inference

David Ruppert, M. P. Wand, Raymond J. Carroll · Cambridge University Press eBooks · 2003

Cited by 1

Inference

Bogdan Pa ¸saniuc, Sriram Sankararaman, Gad Kimmel et al. · 2013

Cited by 0

Inference

Brice Ozenne, Johan Verbeeck · 2025

Statistical inference is concerned with estimating parameters of interest, quantifying the uncertainty of these estimates and testing hypotheses. Chapter 2 introduced four measures of treatment effect and associated estimators: https://www.w3.org/1998/Math/MathML" display="inline"> Θ ^ τ https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003390855/1e8616f2-ef24-44f8-9bd8-4828063f8bac/content/math3_1.tif"/> for the Probabilistic Index, https://www.w3.org/1998/Math/MathML" display="inline"> Δ ^ τ https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003390855/1e8616f2-ef24-44f8-9bd8-4828063f8bac/content/math3_2.tif"/> for the Net Treatment Benefit, https://www.w3.org/1998/Math/MathML" display="inline"> Ψ ^ τ https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003390855/1e8616f2-ef24-44f8-9bd8-4828063f8bac/content/math3_3.tif"/> for the Win Ratio, and https://www.w3.org/1998/Math/MathML" display="inline"> Λ ^ τ https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003390855/1e8616f2-ef24-44f8-9bd8-4828063f8bac/content/math3_4.tif"/> for the Success Odds. When applied to a trial, an estimator will provide an estimate of the treatment effect given the collected data. One could question the reliability of these estimates, especially if the trial included only few participants. The statistical uncertainty surrounding the estimated effect can be addressed through confidence intervals (CIs). CIs can be understood as a range of treatment effect values that are compatible with the data, where compatible is defined relative to a confidence level, typically 95% or https://www.w3.org/1998/Math/MathML" display="inline"> 1 − α https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003390855/1e8616f2-ef24-44f8-9bd8-4828063f8bac/content/math3_5.tif"/> where α is the largest acceptable type I error rate. Formally, if https://www.w3.org/1998/Math/MathML" display="inline"> Θ τ 0 https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003390855/1e8616f2-ef24-44f8-9bd8-4828063f8bac/content/math3_6.tif"/> , https://www.w3.org/1998/Math/MathML" display="inline"> Δ τ 0 https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003390855/1e8616f2-ef24-44f8-9bd8-4828063f8bac/content/math3_7.tif"/> , https://www.w3.org/1998/Math/MathML" display="inline"> Ψ τ 0 https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003390855/1e8616f2-ef24-44f8-9bd8-4828063f8bac/content/math3_8.tif"/> , and https://www.w3.org/1998/Math/MathML" display="inline"> Λ τ 0 https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003390855/1e8616f2-ef24-44f8-9bd8-4828063f8bac/content/math3_9.tif"/> denote the large-sample treatment effect (i.e., the treatment effect that would be estimated in a trial with an infinite number of participants), 95% CIs are constructed such that in 95% of the trials the estimated CI contains the large sample treatment effect.

Cited by 0

• Inference

Michael G. Hudgens, M. Elizabeth Halloran, Nih R Ai · 2008

Cited by 0

Inference

Sanford, A.J. · ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam) · 1991

Cited by 0

Inference.

Luca Giudice (8998823), Ahmed Mohamed (628889), Tarja Malm (3470660) · Figshare · 2024

<p>(A) Scatter plot of the pathways represented by predictive UM-CLL signature PSNs that StellarPath found during training. The X-axis indicates the rank of separability between the two classes. The Y-axis indicates the name of the pathways. The size of the dot depends on the smallest similarity (low percentile of the Separability Power system) between UM-CLL patients which is higher than the highest similarity (high percentile) between M-CLL patients. The color indicates how the UM-CLL subtype is deregulating the pathway. (B) Violin plot of the classification performances assessed comparing the predicted classes of the unknown patients to their true subtype. (C) UM-CLL signature PSN of the activated B Cell Receptor Signaling Pathway of Power 2, where UM-CLL patients are represented by green nodes, M-CLL patients by blue nodes, green lines represent edges between UM-CLL nodes, grey lines represent inter-similarities and blue lines are between M-CLL nodes. A line thickness represents the similarity value associated with it. The size of the node is determined by the patient’s centrality. The PSN is sparse because the edges with low similarity have been hidden. Thanks to StellarPath’s plot function, the PSN represents 123 patients in 20 nodes.</p>

Cited by 0Open access