相关论文: Universality in movie rating distributions

Human feedback is increasingly used across diverse applications like training AI models, developing recommender systems, and measuring public opinion -- with granular feedback often being preferred over binary feedback for its greater…

Let $M_n=\max \left(X_1, X_2, \ldots, X_n \right)$ denote the partial maximum of an independent and identically distributed skew-normal random sequence. In this paper, the rate of uniform convergence of skew-normal extremes is derived. It…

This article gives a formal definition of a lognormal family of probability distributions on the set of symmetric positive definite (PD) matrices, seen as a matrix-variate extension of the univariate lognormal family of distributions. Two…

In classical diffusion, particle step-sizes have a Gaussian distribution. However, in superdiffusion, they have power-law tails, with transport dominated by rare, long L\'evy flights. Similarly, if the time interval between scattering…

Structures with heavy-tailed distributions of disorder occur widely in nature. The evolution of such systems, as in foraging for food or the occurrence of earthquakes is generally analyzed in terms of an incoherent series of events. But the…

Price fluctuations in financial markets can be characterized by L\'evy's stable distribution, which is supported by the generalized central limit system. When the stable parameters were estimated from four different stock markets in long…

Phenomena as diverse as breeding bird populations, the size of U.S. firms, money invested in mutual funds, the GDP of individual countries and the scientific output of universities all show unusual but remarkably similar growth…

We consider families of fast-slow skew product maps of the form \begin{align*} x_{n+1} = x_n+\epsilon a(x_n,y_n,\epsilon), \quad y_{n+1} = T_\epsilon y_n, \end{align*} where $T_\epsilon$ is a family of nonuniformly expanding maps, and prove…

Time series of observables measured from complex systems do often exhibit non-normal statistics, their statistical distributions (PDF's) are not gaussian and often skewed, with roughly exponential tails. Departure from gaussianity is…

In video recommendation systems, user behaviors such as watch time, likes, and follows are commonly used to infer user interest. However, these behaviors are influenced by various biases, including duration bias, demographic biases, and…

The probability distribution of lens image separations is calculated for the ``standard'' gravitational lensing statistics model in an arbitrary, flat Robertson-Walker universe, where lensing galaxies are singular isothermal spheres that…

In terms of the stock exchange returns, we compute the analytic expression of the probability distributions F{DAX,+} and F{DAX,-} of the normalized positive and negative DAX (Germany) index daily returns r(t). Furthermore, we define the…

Modern web-based platforms show ranked lists of recommendations to users, attempting to maximise user satisfaction or business metrics. Typically, the goal of such systems boils down to maximising the exposure probability for items that are…

The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…

This paper presents a simple unsupervised learning algorithm for classifying reviews as recommended (thumbs up) or not recommended (thumbs down). The classification of a review is predicted by the average semantic orientation of the phrases…

We consider skew-product maps over circle rotations $x\mapsto x+\alpha$ (mod 1) with factors that take values in SL(2,R) In numerical experiments with $\alpha$ the inverse golden mean, Fibonacci iterates of almost Mathieu maps with rotation…

We study the evolution of opinions on a directed network with community structure. Individuals update their opinions synchronously based on a weighted average of their neighbors' opinions, their own previous opinions, and external media…

We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…

We present a generalisation of surface photometry to the higher-order moments of the line-of-sight velocity distribution of galaxies observed with integral-field spectrographs. The generalisation follows the approach of surface photometry…

Shepard's universal law of generalization is a remarkable hypothesis about how intelligent organisms should perceive similarity. In its broadest form, the universal law states that the level of perceived similarity between a pair of stimuli…