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Non-linear dimensionality reduction: Riemannian metric estimation and the problem of geometric discovery
Non-linear dimensionality reduction Riemannian metric estimation the problem geometric discovery
2013/6/14
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degre...
Estimating Network Degree Distributions Under Sampling: An Inverse Problem, with Applications to Monitoring Social Media Networks
Estimating Network Degree Distributions Sampling An Inverse Problem Applications Monitoring Social Media Networks
2013/6/14
Networks are a popular tool for representing elements in a system and their interconnectedness. Many observed networks can be viewed as only samples of some true underlying network. Such is frequently...
Online Learning in a Contract Selection Problem
Online Learning Contract Selection Problem
2013/6/14
In an online contract selection problem there is a seller which offers a set of contracts to sequentially arriving buyers whose types are drawn from an unknown distribution. If there exists a profitab...
The subset argument and consistency of MLE in GLMM: Answer to an open problem and beyond
Cramer consistency crossed random effects MLE GLMM,salamander mating data subset argument Wald consistency
2013/4/27
We give answer to an open problem regarding consistency of the maximum likelihood estimators (MLEs) in generalized linear mixed models (GLMMs) involving crossed random effects. The solution to the ope...
Simultaneous Localization and Mapping Problem in Wireless Sensor Networks
Simultaneous localization and Mapping,Indoor localization Received Signal Strength Indicator WiFi Signal Propagation
2012/11/23
Mobile device localization in wireless sensor networks is a challenging task. It has already been addressed when the WiFI propagation maps of the access points are modeled deterministically. However, ...
Higher Variations of the Monty Hall Problem (3.0 and 4.0) and Empirical Definition of the Phenomenon of Mathematics, in Boole's Footsteps, as Something the Brain Does
Artificial Intelligence Binary Structure Boolean Algebra Boolean Operators Boole’s Algebra Brain Science, Cognition Cognitive Science Definition of Mathematics Definition of Probability Theory Digital Mathematics Electrical Engineering, Foundations of Mathematics Human Intelligence, Linguistics, Logic, Monty Hall Problem, Neuroscience Non-quantitative and Quantitative Mathematics Probability Theory Rational Thought and Language
2012/9/17
In Advances in Pure Mathematics (www.scirp.org/journal/apm) , Vol. 1, No. 4 (July 2011), pp.
136-154, the mathematical structure of the much discussed problem of probability known as the Monty Ha...
On characteristics of an ordinary differential equation and a related inverse problem in epidemiology
Chronic disease Compartment model Incidence Mortality Prevalence Population
2012/9/18
In this work we examine the properties of a recently described ordinary differential equation that relates the age-specific prevalence of achronic dis-ease with the incidence and mortalities of the di...
Inverse Modeling of Dynamical Systems: Multi-Dimensional Extensions of a Stochastic Switching Problem
Inverse Modeling of Dynamical Systems Multi-Dimensional Extensions Stochastic Switching Problem
2012/9/18
The Buridan's ass paradox is characterized by perpetual indecision between two states, which are never attained. When this problem is formulated as a dynamical
system, indecision is modeled by a disc...
A simple and numerical stable algorithm for solving the cone projection problem based on a Gram-Schmidt process
cone projection algorithm convexity constraints convexity test simulations Gram-Schmidt
2012/9/19
We are presenting a simple and numerical stable algorithm for the solution of the cone projection problem which is suitable for relative small data sets and for simulation purposes needed for con-vexi...
A procedure for the change point problem in parametric models based on phi-divergence test-statistics
Change point Information criterion Divergence Wald test-statistic
2011/7/19
This paper studies the change point problem for a general parametric, univariate or multivariate family of distributions.
PAC learnability under non-atomic measures: a problem by Vidyasagar
PAC learnability non-atomic measures learning rule uniform GlivenkoCantelli classes Martin’s Axiom VC dimension modulo countable sets fat shattering dimension modulo countable sets
2011/6/20
In response to a 1997 problem of M. Vidyasagar, we state a criterion for PAC learnability of a concept
class C under the family of all non-atomic (diffuse) measures on the domain
. The uniform Gliv...
Optimal Multistage Sampling in a Boundary-Crossing Problem
Asymptotic Brownian motion Group sequential Multistage Optimality
2011/6/17
Brownian motion with known positive drift is sampled in stages until
it crosses a positive boundary a. A family of multistage samplers that con-
trol the expected overshoot over the boundary by vary...
Uncertainty quantification and weak approximation of an elliptic inverse problem
Uncertainty quantification weak approximation elliptic inverse problem
2011/3/18
We consider the inverse problem of determining the permeability from the pressure in a Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion coefficient for a lin...
Scale invariance versus translation variance in Nash bargaining problem
Scale invariance translation variance Nash bargaining problem
2011/3/18
Nash’s solution in his celebrated article on the bargaining problem calling for
maximization of product of marginal utilities is revisited; a different line of
argument supporting such a solution ...
Nonsmooth Formulation of the Support Vector Machine for a Neural Decoding Problem
Optimization and Control (math.OC) Numerical Analysis (math.NA) Statistics Theory (math.ST)
2010/12/17
This paper formulates a generalized classification algorithm with an application to classifying (or `decoding') neural activity in the brain. Medical doctors and researchers have long been interested ...