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When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts?
Non-Negative Matrix Factorization Parts
2015/8/21
We interpret non-negative matrix factorization geometrically, as the
problem of finding a simplicial cone which contains a cloud of data
points and which is contained in the positive orthant.
Fast Solution of `1-norm Minimization Problems When the Solution May be Sparse
LASSO. LARS Homotopy Methods Basis Pursuit.
2015/8/21
The minimum `1-norm solution to an underdetermined system of linear equations y = Ax,
is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property
is of interest i...
Multiscale Representations for Manifold-Valued Data
Symmetric Space Lie Group Two-Scale Refi nement Scheme
2015/8/21
We describe multiscale representations for data observed on equispaced grids and taking
values in manifolds such as: the sphere S2, the special orthogonal group SO(3), the positive
definite ma...
Most quasi-Monte Carlo research focuses on sampling from the unit
cube. Many problems, especially in computer graphics, are de ned via
quadrature over the unit triangle. Quasi-Monte Carlo methods fo...
Let Y be a binary random variable and X a scalar. Let ^ be the
maximum likelihood estimate of the slope in a logistic regression of Y on
X with intercept. Further let x0 and x1 be the average of ...
Guaranteed Conservative Fixed Width Confidence Intervals Via Monte Carlo Sampling
Intervals Via Monte Carlo Sampling Guaranteed Conservative
2015/8/21
Monte Carlo methods are used to approximate the means, μ, of random variables
Y, whose distributions are not known explicitly. The key idea is that the average of a random
sample, Y1,...,Yn, tends t...
The Future of Indirect Evidence
statistical learning experience of others Bayesian and frequentist
2015/8/20
Familiar statistical tests and estimates are obtained by the direct observation of cases of
interest: a clinical trial of a new drug, for instance, will compare the drug's e ects on a relevant set of...
Correlated z-values and the accuracy of large-scale statistical estimates
large-scale statistical estimates Correlated z-values
2015/8/20
We consider large-scale studies in which there are hundreds or thousands of correlated cases to investigate, each represented by its own normal variate, typically a
z-value. A familiar example is pro...
MULTISCALE MAXIMUM LIKELIHOOD ANALYSIS OF A SEMIPARAMETRIC MODEL, WITH APPLICATIONS
LIKELIHOOD ANALYSIS SEMIPARAMETRIC MODEL WITH APPLICATIONS
2015/8/20
A special semiparametric model for a univariate density is introduced
that allows analyzing a number of problems via appropriate transformations. Two problems treated in some detail are testing for t...
OPTIMAL AND FAST DETECTION OF SPATIAL CLUSTERS WITH SCAN STATISTICS
SPATIAL CLUSTERS SCAN STATISTICS
2015/8/20
We consider the detection of multivariate spatial clusters in the Bernoulli
model with N locations, where the design distribution has weakly dependent
marginals. The locations are scanned with a rec...
Inference and Modeling with Log-concave Distributions
Log-concave Distributions Inference and Modeling
2015/8/20
Log-concave distributions are an attractive choice for modeling
and inference, for several reasons: The class of log-concave distributions contains most of the commonly used parametric distributions ...
In this paper, the quantum logical ‘or’ is analyzed from a physical perspective.
We show that it is the existence of EPR-like correlation states for the quantum
mechanical entity under consideration...
THE DISTRIBUTION OF LEADING DIGITS AND UNIFORM DISTRIBUTION MOD
Arithmetic sequence theory triangular array coefficient of letters
2015/7/15
The lead digit behavior of a large class of arithmetic sequences is de-
termined by using results from the theory of uniform distribution mod I.
Theory for triangular arrays is developed and appli...
DE FINETTI'S THEOREM FOR MARKOV CHAINS.