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Adaptive Priors based on Splines with Random Knots
Adaptive estimation bayesian non-parametric optimal contrac-tion rate spline random knots
2013/4/27
Splines are useful building blocks when constructing priors on nonparametric models indexed by functions. Recently it has been established in the literature that hierarchical priors based on splines w...
A Greedy Approximation of Bayesian Reinforcement Learning with Probably Optimistic Transition Model
Reinforcement Learning Uncertain Knowledge Probabilistic Reasoning Optimal Behavior in Polynomial Time
2013/5/2
Bayesian Reinforcement Learning (RL) is capable of not only incorporating domain knowledge, but also solving the exploration-exploitation dilemma in a natural way. As Bayesian RL is intractable except...
On near(est) correlation matrix
Correlation matrix positive semidefinite matrix matrix nearness problem versal deformations of matrices
2013/4/27
We present an elementary heuristic reasoning based on Arnold's theory of versal deformations in support of a straightforward algorithm for finding a correlation matrix near the given symmetric one.
Estimation Stability with Cross Validation (ESCV)
Lasso model selection parameter estimation prediction
2013/4/27
Cross-validation (CV) is often used to select the regularization parameter in high dimensional problems. However, when applied to the sparse modeling method Lasso, CV leads to models that are unstable...
Consider approximating a function $f$ by an emulator $\hat{f}$ based on $n$ observations of $f$. This problem is a common when observing $f$ requires a computationally demanding simulation or an actua...
Simultaneous L^2- and L^inf-Adaptation in Nonparametric Regression
Adaptive estimation nonparametric regression thresholding wavelets
2013/4/27
Consider the nonparametric regression framework. It is a classical result that the minimax rates for L^2- and L^inf-risk over a H\"older ball with smoothness index \beta are n^(-\beta/(2\beta+1)) and ...
A Unified Framework for Probabilistic Component Analysis
A Unified Framework Probabilistic Component Analysis
2013/5/2
In this paper, we present a unifying framework which reduces the construction of probabilistic component analysis techniques to a mere selection of the latent neighbourhood via the prior, thus providi...
Toward Optimal Stratification for Stratified Monte-Carlo Integration
Toward Optimal Stratification Stratified Monte-Carlo Integration
2013/4/27
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a noisy function, given a finite budget n of noisy evaluations to the function. We tackle in this paper the probl...
Optimal design for linear models with correlated observations
Optimal design correlated observations integral operator,eigenfunctions arcsine distribution logarithmic potential
2013/4/27
In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for...
Understanding Operational Risk Capital Approximations: First and Second Orders
Basel II/III Capital Approximation Loss Distributional Approach Capital Approximation Value-at-Risk Expected Shortfall Spectral Risk Measure Subexponential Regularly Varying
2013/5/2
We set the context for capital approximation within the framework of the Basel II / III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. ...
Refinement revisited with connections to Bayes error, conditional entropy and calibrated classifiers
Refinement Score Probability Elicitation Calibrated Classifier Bayes Error Bound Conditional Entropy Proper Loss
2013/4/27
The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space i...
Infinite-dimensional Bayesian filtering for detection of quasi-periodic phenomena in spatio-temporal data
Infinite-dimensional Bayesian filtering detection of quasi-periodic phenomena spatio-temporal data
2013/4/27
This paper introduces a spatio-temporal resonator model and an inference method for detection and estimation of nearly periodic temporal phenomena in spatio-temporal data. The model is derived as a sp...
Visualizing and Interacting with Concept Hierarchies
Information visualization Formal Concept Analysis Galois sub-hierarchy
2013/4/27
Concept Hierarchies and Formal Concept Analysis are theoretically well grounded and largely experimented methods. They rely on line diagrams called Galois lattices for visualizing and analysing object...
Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo
Information visualization Formal Concept Analysis Galois sub-hierarchy
2013/4/27
In [Chen, D., Owen, Ann. Stat., 39, 673--701, 2011] Markov chain Monte Carlo (MCMC) was studied under the assumption that the driver sequence is a deterministic sequence rather than independent U(0,1)...
We show that numerical data assimilation is feasible in principle for an idealized model only if an effective dimension of the noise is bounded; this effective dimension is bounded when the noises in ...