scholarly journals Approaching probabilistic laws

Synthese ◽  
2021 ◽  
Author(s):  
Ilkka Niiniluoto
Keyword(s):  
Probability Distributions ◽  
Distance Measures ◽  
State Spaces ◽  
New Class ◽  
Order Language ◽  
Continuous State ◽  
Structure Description ◽  
Physical Necessity ◽  
Universal Law ◽  
Jensen Shannon Divergence

AbstractIn the general problem of verisimilitude, we try to define the distance of a statement from a target, which is an informative truth about some domain of investigation. For example, the target can be a state description, a structure description, or a constituent of a first-order language (Sect. 1). In the problem of legisimilitude, the target is a deterministic or universal law, which can be expressed by a nomic constituent or a quantitative function involving the operators of physical necessity and possibility (Sect. 2). The special case of legisimilitude, where the target is a probabilistic law (Sect. 3), has been discussed by Roger Rosenkrantz (Synthese, 1980) and Ilkka Niiniluoto (Truthlikeness, 1987, Ch. 11.5). Their basic proposal is to measure the distance between two probabilistic laws by the Kullback–Leibler notion of divergence, which is a semimetric on the space of probability measures. This idea can be applied to probabilistic laws of coexistence and laws of succession, and the examples may involve discrete or continuous state spaces (Sect. 3). In this paper, these earlier studies are elaborated in four directions (Sect. 4). First, even though deterministic laws are limiting cases of probabilistic laws, the target-sensitivity of truthlikeness measures implies that the legisimilitude of probabilistic laws is not easily reducible to the deterministic case. Secondly, the Jensen-Shannon divergence is applied to mixed probabilistic laws which entail some universal laws. Thirdly, a new class of distance measures between probability distributions is proposed, so that their horizontal differences are taken into account in addition to vertical ones (Sect. 5). Fourthly, a solution is given for the epistemic problem of estimating degrees of probabilistic legisimilitude on the basis of empirical evidence (Sect. 6).

scholarly journals minicore: Fast scRNA-seq clustering with various distances

2021 ◽  
Author(s):  
Daniel N. Baker ◽  
Nathan Dyjack ◽  
Vladimir Braverman ◽  
Stephanie C. Hicks ◽  
Ben Langmead
Keyword(s):  
Open Source ◽  
Count Data ◽  
Probability Distributions ◽  
Expression Profiles ◽  
Distance Measures ◽  
Bhattacharyya Distance ◽  
Link Type ◽  
Leibler Divergence ◽  
Careful Handling ◽  
Jensen Shannon Divergence

AbstractSingle-cell RNA-sequencing (scRNA-seq) analyses typically begin by clustering a gene-by-cell expression matrix to empirically define groups of cells with similar expression profiles. We describe new methods and a new open source library, minicore, for efficient k-means++ center finding and k-means clustering of scRNA-seq data. Minicore works with sparse count data, as it emerges from typical scRNA-seq experiments, as well as with dense data from after dimensionality reduction. Minicore’s novel vectorized weighted reservoir sampling algorithm allows it to find initial k-means++ centers for a 4-million cell dataset in 1.5 minutes using 20 threads. Minicore can cluster using Euclidean distance, but also supports a wider class of measures like Jensen-Shannon Divergence, Kullback-Leibler Divergence, and the Bhattacharyya distance, which can be directly applied to count data and probability distributions.Further, minicore produces lower-cost centerings more efficiently than scikit-learn for scRNA-seq datasets with millions of cells. With careful handling of priors, minicore implements these distance measures with only minor (<2-fold) speed differences among all distances. We show that a minicore pipeline consisting of k-means++, localsearch++ and minibatch k-means can cluster a 4-million cell dataset in minutes, using less than 10GiB of RAM. This memory-efficiency enables atlas-scale clustering on laptops and other commodity hardware. Finally, we report findings on which distance measures give clusterings that are most consistent with known cell type labels.AvailabilityThe open source library is at https://github.com/dnbaker/minicore. Code used for experiments is at https://github.com/dnbaker/minicore-experiments.

scholarly journals A New Improved Penalty Avoiding Rational Policy Making Algorithm for Keepaway with Continuous State Spaces

2009 ◽  
Vol 13 (6) ◽  
pp. 675-682 ◽  
Author(s):  
Takuji Watanabe ◽  
◽  
Kazuteru Miyazaki ◽  
Hiroaki Kobayashi ◽  
◽  
...  
Keyword(s):  
Basis Function ◽  
Function Approximation ◽  
Policy Making ◽  
Basis Functions ◽  
State Spaces ◽  
Soccer Game ◽  
Continuous State ◽  
Current Input ◽  
Multiagent Environments ◽  
Parp 1

The penalty avoiding rational policy making algorithm (PARP) [1] previously improved to save memory and cope with uncertainty, i.e., IPARP [2], requires that states be discretized in real environments with continuous state spaces, using function approximation or some other method. Especially, in PARP, a method that discretizes state using a basis functions is known [3]. Because this creates a new basis function based on the current input and its next observation, however, an unsuitable basis function may be generated in some asynchronous multiagent environments. We therefore propose a uniform basis function and range extent of the basis function is estimated before learning. We show the effectiveness of our proposal using a soccer game task called “Keepaway.”

Stable running of a planar underactuated biped robot

Robotica ◽  
2010 ◽  
Vol 29 (5) ◽  
pp. 657-665 ◽  
Author(s):  
Yong Hu ◽  
Gangfeng Yan ◽  
Zhiyun Lin
Keyword(s):  
Limit Cycle ◽  
Stance Phase ◽  
Control Strategies ◽  
Basin Of Attraction ◽  
Biped Robot ◽  
State Spaces ◽  
Continuous State ◽  
Event Based ◽  
Telescopic Legs ◽  
The Basin Of Attraction

SUMMARYThis paper investigates the stable-running problem of a planar underactuated biped robot, which has two springy telescopic legs and one actuated joint in the hip. After modeling the robot as a hybrid system with multiple continuous state spaces, a natural passive limit cycle, which preserves the system energy at touchdown, is found using the method of Poincaré shooting. It is then checked that the passive limit cycle is not stable. To stabilize the passive limit cycle, an event-based feedback control law is proposed, and also to enlarge the basin of attraction, an additive passivity-based control term is introduced only in the stance phase. The validity of our control strategies is illustrated by a series of numerical simulations.

Martin's axiom in the model theory of LA

1980 ◽  
Vol 45 (1) ◽  
pp. 172-176
Author(s):  
W. Richard Stark
Keyword(s):  
Model Theory ◽  
Equivalence Theorem ◽  
Compactness Theorem ◽  
Compactness Result ◽  
First Order ◽  
Martin's Axiom ◽  
New Class ◽  
Martin’S Axiom ◽  
Order Language ◽  
Omitting Types

Working in ZFC + Martin's Axiom we develop a generalization of the Barwise Compactness Theorem which holds in languages of cardinality less than . Next, using this compactness theorem, an omitting types theorem for fewer than types is proved. Finally, in ZFC, we prove that this compactness result implies Martin's Axiom (the Equivalence Theorem). Our compactness theorem applies to a new class of theories—ccΣ-theories—which generalize the countable Σ-theories of Barwise's theorem. The Omitting Types Theorem and the Equivalence Theorem serve as examples illustrating the use of ccΣ-theories.Assume = (A, ε) or = (A, ε R1,…,Rm) where is admissible. L() is the first-order language with constants for elements of A and relation symbols for relations in . LA is A ⋂ L∞ω where the L of L∞ω is any language in A. A theory T in LA is consistent if there is no derivation in A of a contradiction from T. is LA with new constants ca for each a and A. The basic terms of consist of the constants of and the terms f(ca1,…,cam) built directly from constants using functions f of . The symbol t is used for basic terms. A theory T in LA is Σ if it is defined by a formula of L(). The formula φ⌝ is a logical equivalent of ¬φ defined by: (1) φ⌝ = ¬φ if φ is atomic; (2) (¬φ)⌝ = φ (3) (⋁φ∈Φ φ)⌝ = ⋀φ∈Φ φ⌝; (4) (⋀φ∈Φ φ) ⋁φ∈Φ φ⌝; (5) (∃χφ(x))⌝ ∀χφ⌝(x); ∀χφ(x))⌝ = ∃χφ⌝(x).

scholarly journals Probability of ruin in discrete insurance risk model with dependent Pareto claims

2019 ◽  
Vol 7 (1) ◽  
pp. 215-233
Author(s):  
Corina D. Constantinescu ◽  
Tomasz J. Kozubowski ◽  
Haoyu H. Qian
Keyword(s):  
Power Law ◽  
Pareto Distribution ◽  
Risk Model ◽  
Probability Distributions ◽  
Insurance Risk ◽  
Probability Of Ruin ◽  
New Class ◽  
Compound Binomial ◽  
Compound Binomial Risk Model ◽  
Positive Integers

AbstractWe present basic properties and discuss potential insurance applications of a new class of probability distributions on positive integers with power law tails. The distributions in this class are zero-inflated discrete counterparts of the Pareto distribution. In particular, we obtain the probability of ruin in the compound binomial risk model where the claims are zero-inflated discrete Pareto distributed and correlated by mixture.

scholarly journals An Extension of the Rational Policy Making algorithm to Continuous State Spaces

2007 ◽  
Vol 22 ◽  
pp. 332-341 ◽  
Author(s):  
Kazuteru Miyazaki ◽  
Hajime Kimura ◽  
Shigenobu Kobayashi
Keyword(s):  
Policy Making ◽  
State Spaces ◽  
Continuous State
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