Related papers: Approximation by random fractions
We prove decidability results on the existence of constant subsequences of uniformly recurrent morphic sequences along arithmetic progressions. We use spectral properties of the subshifts they generate to give a first algorithm deciding…
Some practical results are derived for population inference based on a sample, under the two qualitative conditions of 'ignorability' and exchangeability. These are the 'Histogram Theorem', for predicting the outcome of a non-sampled member…
We seek to find normative criteria of adequacy for nonmonotonic logic similar to the criterion of validity for deductive logic. Rather than stipulating that the conclusion of an inference be true in all models in which the premises are…
We attempt to dissolve the measurement problem using an anthropic principle which allows us to invoke rational observers. We argue that the key feature of such observers is that they are rational (we need not care whether they are…
Extending our own and others' earlier approaches to reasoning about termination of probabilistic programs, we propose and prove a new rule for termination with probability one, also known as "almost-certain termination". The rule uses both…
Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are independent and identically distributed…
First, we prove a \emph{local almost sure central limit theorem} for lattice random walks in the plane. The corresponding version for random walks in the line was considered by the author in \cite{5}. This gives us a quantitative version of…
A regression model is proposed for the analysis of an ordinal response variable depending on a set of multiple covariates containing ordinal and potentially other variables. The proportional odds model (McCullagh (1980)) is used for the…
We outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained resorting to maximum entropy technique, under the…
We show that the probability of a site being occupied at any instance of time in the one-dimensional randomly fluctuating hyperrectangles processes decreases monotonically with respect to its distance from the origin.
We want to select the best systems out of a given set of systems (or rank them) with respect to their expected performance. The systems allow random observations only and we assume that the joint observation of the systems has a…
The paper addresses the problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under two standard kinds of assumptions --…
We give a reciprocity formula for a two-variable sum where the variables satisfy a linear congruence condition. We also prove that such sum is a measure of how well a rational is approximable from below and show that the reciprocity formula…
We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…
Let $E\subset [0,1)^{d}$ be a set supporting a probability measure $\mu$ with Fourier decay $|\widehat{\mu}({\bf{t}})|\ll (\log |{\bf{t}}|)^{-s}$ for some constant $s>d+1.$ Consider a sequence of expanding integral matrices…
In a prequential approach to algorithmic randomness, probabilities for the next outcome can be forecast `on the fly' without the need for fully specifying a probability measure on all possible sequences of outcomes, as is the case in the…
Prediction without justification has limited applicability. As a remedy, we learn to extract pieces of input text as justifications -- rationales -- that are tailored to be short and coherent, yet sufficient for making the same prediction.…
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…