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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：erration split-plot designs via complementary sets when the whole plot factors are important
图因子 互补集 错误分割图设计
2023/5/15
In practice, fractional factorial split-plot (FFSP) designs are widely used when the levels of some factors are very difficult to change or control. The factors of an FFSP design are divided into two ...
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.
Higher Criticism Thresholding: Optimal Feature Selection when Useful Features are Rare and Weak
Criticism Thresholding Feature Selection
2015/8/21
Linear classi cation analysis is a fundamental tool for science
and technology. In important application elds today { genomics and proteomics are examples { one automatically obtains very high-dimen...
COUNTING FACES OF RANDOMLY-PROJECTED POLYTOPES WHEN THE PROJECTION RADICALLY LOWERS DIMENSION
RANDOMLY-PROJECTED RADICALLY LOWERS DIMENSION
2015/8/21
The modern trend in statistics and probability is to consider the case where both
the number of dimensions d and the sample size n are large [19, 21]. In that case, the
intuition fostered by the cla...
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...
DISCUSSION:THE DANTZIG SELECTOR:STATISTICAL ESTIMATION WHEN p IS MUCH LARGER THAN n
DANTZIG SELECTOR STATISTICAL ESTIMATION p IS MUCH LARGER THAN n
2015/8/21
This is a fascinating paper on an important topic: the choice of predictor variables in large-scale linear models. A previous paper in these pages attacked the same problem using the “LARS” algorithm ...
Simultaneous Inference: When Should Hypothesis Testing Problems Be Combined?
Simultaneous Inference Testing Problems
2015/8/20
Modern statisticians are often presented with hundreds or thousands of hypothesis
testing problems to evaluate at the same time, generated from new scientific technologies such as microarrays, ...
Deconstructing Javanese Batik Motif:When Traditional Heritage Meets Computation
batik fractal attractor iterated function system affine transformation,
2015/7/28
The paper discusses some aspects of Iterated Function System while referring to some interesting point of view into Indonesian traditional batik. The deconstruction is delivered in our recognition of ...
Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns
Solving Quadratic Equations PhaseLift Many Equations Unknowns
2015/6/17
This note shows that we can recover any complex vector x0 ∈ Cn exactly from on the order of n quadratic equations of the form |hai, x0i|2 = bi, i = 1, . . . , m, by using a semidefinite program known ...
Sparse Covariance Estimation When Variables are Ordered
Sparse Covariance Estimation Variables Ordered
2015/3/20
Sparse Covariance Estimation When Variables are Ordered.
Optimal Control of dams using P(M,Lambda,tau) policies when the input process is an inverse Gaussian process
Optimal Control of dams P(M,Lambda,tau) policies When the input process inverse Gaussian process
2012/11/23
We consider the P(M,lambda,tau) maintenance policy of a dam using the total discounted and long-run average costs, when the input process is inverse Gaussian.
We are interested in classifying those sets of primes P such that when we sieve out the integers up to x by the primes in P^c we are left with roughly the expected number of unsieved integers. In part...
Notes on area operator, geometric 2-rough paths and Young integral when p^-1+q^-1=1
Notes area operator geometric 2-rough paths Young integral
2012/4/17
1.When equipped with 2-rough norm and restricted to continuous paths with bounded variation, the area operator is a closable unbounded operator. 2.The area defined through Riemann-Stieltjes integral i...
$Top(X)$ within $\px$ ]{When lattices meet topology: $Top(X)$ within $\px$.}
$Top(X)$ within $\px$ lattices meet topology
2012/2/29
For a non-empty set $X$, the collection $Top(X)$ of all topologies on $X$ sits inside the Boolean lattice $\PP(\PP(X))$ (when ordered by set-theoretic inclusion) which in turn can be naturally identif...
There always exists at least one prime between x and x+x^{1/2} when x is sufficiently large
Pprime distribution of primes
2011/9/21
In this paper one has shown that there always exists at least one pseudo prime number between x and x+x^{1/2} when x is sufficiently large for a pseudo sequence of odd numbers, so it also is true that...