Related papers: Quantization for a mixture of uniform distribution…
Quantum circuits generating probability distributions has applications in several areas. Areas like finance require quantum circuits that can generate distributions that mimic some given data pattern. Hamiltonian simulations require…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
In this paper we provide a method for constructing joint distributions for an arbitrary set of observables on finite dimensional Hilbert spaces irrespective of whether the observables commute or not. These distributions have a number of…
Quantification is the machine learning task of estimating test-data class proportions that are not necessarily similar to those in training. Apart from its intrinsic value as an aggregate statistic, quantification output can also be used to…
Majorization provides a rather powerful partial-order classification of probability distributions depending only on the spread of the statistics, and not on the actual numerical values of the variable being described. We propose to apply…
Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to…
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. In this paper, we have considered a Borel probability measure…
We consider the probability by which quantum phase measurements of a given precision can be done successfully. The least upper bound of this probability is derived and the associated optimal state vectors are determined. The probability…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
Although an input distribution may not majorize a target distribution, it may majorize a distribution which is close to the target. Here we introduce a notion of approximate majorization. For any distribution, and given a distance $\delta$,…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
Quantization of a probability measure means representing it with a finite set of Dirac masses that approximates the input distribution well enough (in some metric space of probability measures). Various methods exists to do so, but the…
Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
Quantization summarizes continuous distributions by calculating a discrete approximation. Among the widely adopted methods for data quantization is Lloyd's algorithm, which partitions the space into Vorono\"i cells, that can be seen as…
In a mathematical context in which one can multiply distributions the "`formal"' nonperturbative canonical Hamiltonian formalism in Quantum Field Theory makes sense mathematically, which can be understood a priori from the fact the so…
In this paper, we have considered a uniform distribution on a regular polygon with $k$-sides for some $k\geq 3$ and the set of all its $k$ vertices as a conditional set. For the uniform distribution under the conditional set first, for all…
Quantile matching is a strictly monotone transformation that sends the observed response values $\{y_1, . . . , y_n\}$ to the quantiles of a given target distribution. A likelihood based criterion is developed for comparing one target…
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…