Related papers: Models of real-valued measurability
This work includes a new characterization of the multivariate normal distribution. In particular, it is shown that a positive density function $f$ is Gaussian if and only if the $f(x+ y)/f(x)$ is convex in $x$ for every $y$. This result has…
In recent years, there has been increasing interest in explanation methods for neural model predictions that offer precise formal guarantees. These include abductive (respectively, contrastive) methods, which aim to compute minimal subsets…
This paper deals with some computational aspects in the Bayesian analysis of statistical models with intractable normalizing constants. In the presence of intractable normalizing constants in the likelihood function, traditional MCMC…
We construct a new kind of measures, called projection families, which generalize the classical notion of vector and operator-valued measures. The maximal class of reasonable functions admits an integral with respect to a projection family,…
Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…
Let A be a standard Borel space, and consider the space A^{\bbN^{(k)}} of A-valued arrays indexed by all size-k subsets of \bbN. This paper concerns random measures on such a space whose laws are invariant under the natural action of…
Classical versions of Kolmogorov complexity are incomputable. Nevertheless, in 1975 Solovay showed that there are computable functions $f > K+O(1)$ such that for infinitely many strings $\sigma$, $f(\sigma)=K(\sigma)+O(1)$, where $K$…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
We establish a Sharkovskii-type theorem for a class of discrete random dynamical systems via the random Conley index. Using the continuation property of the Conley index, we extend classical forcing results to random systems obtained from…
This paper investigates the possibility of constructive extraction of measurable selector from set-valued maps which may commonly arise in viability theory, optimal control, discontinuous systems etc. For instance, existence of solutions to…
The validity OF a causal model can be tested ONLY IF the model imposes constraints ON the probability distribution that governs the generated data. IN the presence OF unmeasured variables, causal models may impose two types OF constraints :…
A circle, centered at the origin and with radius chosen so that it has non-empty intersection with the integer lattice $\mathbb{Z}^{2}$, gives rise to a probability measure on the unit circle in a natural way. Such measures, and their weak…
In J. Symbolic Logic,51(4): 957-968, 1986, Pawlikowski proved that, if $r$ is a random real over $\mathbf{N}$, and $c$ is Cohen real over $\mathbf{N}[r]$, then (a) in $\mathbf{N}[r][c]$ there is a Cohen real over $\mathbf{N}[c]$, and (b)…
Mean Field inference is central to statistical physics. It has attracted much interest in the Computer Vision community to efficiently solve problems expressible in terms of large Conditional Random Fields. However, since it models the…
Systematic differences in experimental materials, methods, measurements, and data handling between labs, over time, and among personnel can sabotage experimental reproducibility. Uncovering such differences can be difficult and time…
Rotational invariance of physical laws is a generally accepted principle. We show that it leads to an additional external constraint on local realistic models of physical phenomena involving measurements of multiparticle spin 1/2…
Machine learning applications often require calibrated predictions, e.g. a 90\% credible interval should contain the true outcome 90\% of the times. However, typical definitions of calibration only require this to hold on average, and offer…
The bootstrap, introduced by Efron (1982), has become a very popular method for estimating variances and constructing confidence intervals. A key insight is that one can approximate the properties of estimators by using the empirical…
Solovay's arithmetical completeness theorem states that the modal logic of provability coincides with the modal logic $\mathbf{GL}$. Hamkins and L\"owe studied the modal logical aspects of set theoretic multiverse and proved that the modal…
Computing observables from conditioned dynamics is typically computationally hard, because, although obtaining independent samples efficiently from the unconditioned dynamics is usually feasible, generally most of the samples must be…