Related papers: A bang-bang principle for the conditional expectat…
This paper is concerned with the study of the consistency of a variational method for probability measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The…
Borrowing the idea of topological pressure determining measure-theoretical entropy in topological dynamical systems, we establish a variational principle for upper metric mean dimension with potential in terms of upper measure-theoretical…
Establishing that a demand mapping is injective is core first step for a variety of methodologies. When a version of the law of demand holds, global injectivity can be checked by seeing whether the demand mapping is constant over any line…
This paper begins with a general theory of error in cross-validation testing of algorithms for supervised learning from examples. It is assumed that the examples are described by attribute-value pairs, where the values are symbolic.…
Strong and fast "bang-bang" (BB) pulses have been recently proposed as a means for reducing decoherence in a quantum system. So far theoretical analysis of the BB technique relied on model Hamiltonians. Here we introduce a method for…
We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…
The principle of the common cause claims that if an improbable coincidence has occurred, there must exist a common cause. This is generally taken to mean that positive correlations between non-causally related events should disappear when…
We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence…
We demonstrate an intuitive relation between conditional entropy and conditional expectation that is useful when one want to compare them as measurement tools to evaluate secrecy systems. In particular, we give a Security Property…
Typically, point forecasting methods are compared and assessed by means of an error measure or scoring function, such as the absolute error or the squared error. The individual scores are then averaged over forecast cases, to result in a…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
The definition of the conditional probability is very important in the theory of the probability. This definition is based on the fact, that random events can be simultaneously measurable. This paper deal with the problem of conditioning…
The linear conditional expectation (LCE) provides a best linear (or rather, affine) estimate of the conditional expectation and hence plays an important r\^ole in approximate Bayesian inference, especially the Bayes linear approach. This…
In this paper, we show that the conditional expectation of a random variable with finite second moment given a $\sigma$-algebra is the unique critical point of an energy functional in Hilbert space $L^2$. Then, we extend by density the…
Decision making or scientific discovery pipelines such as job hiring and drug discovery often involve multiple stages: before any resource-intensive step, there is often an initial screening that uses predictions from a machine learning…
Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on…
Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the support are…
Because high-quality data is like oxygen for AI systems, effectively eliciting information from crowdsourcing workers has become a first-order problem for developing high-performance machine learning algorithms. Two prevalent paradigms,…
Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We…
We show on theoretical grounds that, even in the presence of noise, probabilistic measurement strategies (which have a certain probability of failure or abstention) can provide, upon a heralded successful outcome, estimates with a precision…