相关论文: Proper local scoring rules
Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…
We investigate the flowing behavior of dense suspensions of non-colloidal particles, by coupling macroscopic rheometric experiments and local velocity and concentration measurements through MRI techniques. We find that the flow is localized…
Proper scoring rules elicit truth-telling when making predictions, or otherwise revealing information. However, when multiple predictions are made of the same event, telling the truth is in general no longer optimal, as agents are motivated…
In this paper we introduce a novel objective prior distribution levering on the connections between information, divergence and scoring rules. In particular, we do so from the starting point of convex functions representing information in…
Learning DAG structures from purely observational data remains a long-standing challenge across scientific domains. An emerging line of research leverages the score of the data distribution to initially identify a topological order of the…
Score estimation is the backbone of score-based generative models (SGMs), especially denoising diffusion probabilistic models (DDPMs). A key result in this area shows that with accurate score estimates, SGMs can efficiently generate samples…
Diffusion models are state-of-the-art tools for various generative tasks. Yet training these models involves estimating high-dimensional score functions, which in principle suffers from the curse of dimensionality. It is therefore important…
Many forecasts consist not of point predictions but concern the evolution of quantities. For example, a central bank might predict the interest rates during the next quarter, an epidemiologist might predict trajectories of infection rates,…
We consider sequences of random variables whose probability generating functions are polynomials all of whose roots lie on the unit circle. The distribution of such random variables has only been sporadically studied in the literature. We…
Log-density gradient estimation is a fundamental statistical problem and possesses various practical applications such as clustering and measuring non-Gaussianity. A naive two-step approach of first estimating the density and then taking…
This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or…
We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…
Sequential estimation of a vector of linear regression coefficients is considered under both centralized and decentralized setups. In sequential estimation, the number of observations used for estimation is determined by the observed…
We consider the design of systems for sequential decentralized detection, a problem that entails several interdependent choices: the choice of a stopping rule (specifying the sample size), a global decision function (a choice between two…
We derive a necessary and sufficient condition for the sum of M independent continuous random variables modulo 1 to converge to the uniform distribution in L^1([0,1]), and discuss generalizations to discrete random variables. A consequence…
If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…
Representing probability distributions by the gradient of their density functions has proven effective in modeling a wide range of continuous data modalities. However, this representation is not applicable in discrete domains where the…
We analyze the steady-state flow as a function of the initial density for a class of deterministic cellular automata rules (``traffic rules'') with periodic boundary conditions [H. Fuks and N. Boccara, Int. J. Mod. Phys. C 9, 1 (1998)]. We…
Decision trees built with data remain in widespread use for nonparametric prediction. Predicting probability distributions is preferred over point predictions when uncertainty plays a prominent role in analysis and decision-making. We study…
Given an $n$-sample of random vectors $(X_i,Y_i)_{1 \leq i \leq n}$ whose joint law is unknown, the long-standing problem of supervised classification aims to \textit{optimally} predict the label $Y$ of a given a new observation $X$. In…