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We provide a new algorithmic framework for differentially private estimation of general functions that adapts to the hardness of the underlying dataset. We build upon previous work that gives a paradigm for selecting an output through the…
Extreme value theory has constructed asymptotic properties of the sample maximum. This study concerns probability distribution estimation of the sample maximum. The traditional approach is parametric fitting to the limiting distribution --…
Preference Optimization (PO), is gaining popularity as an alternative choice of Proximal Policy Optimization (PPO) for aligning Large Language Models (LLMs). Recent research on aligning LLMs iteratively with synthetic or partially synthetic…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
Inverse probability weighting (IPW) is a general tool in survey sampling and causal inference, used both in Horvitz-Thompson estimators, which normalize by the sample size, and H\'ajek/self-normalized estimators, which normalize by the sum…
In the present work, we provide the general expression of the normalized centered moments of the Fr\'echet extreme-value distribution. In order to try to represent a set of data corresponding to rare events by a Fr\'echet distribution, it…
Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…
Performative prediction aims to model scenarios where predictive outcomes subsequently influence the very systems they target. The pursuit of a performative optimum (PO) -- minimizing performative risk -- is generally reliant on modeling of…
In data analysis, unexpected results often prompt researchers to revisit their procedures to identify potential issues. While some researchers may struggle to identify the root causes, experienced researchers can often quickly diagnose…
Traditional risk factors like beta, size/value, and momentum often lag behind market dynamics in measuring and predicting stock return volatility. Statistical models like PCA and factor analysis fail to capture hidden nonlinear…
Zipf's law states that sequential frequencies of words in a text correspond to a power function. Its probabilistic model is an infinite urn scheme with asymptotically power distribution. The exponent of this distribution must be estimated.…
I proposed (8, 1, 3) that p values should be supplemented by an estimate of the false positive risk (FPR). FPR was defined as the probability that, if you claim that there is a real effect on the basis of p value from a single unbiased…
In this paper, we present a study of an a posteriori estimator for the discretization error of a non-standard finite difference scheme applied to boundary value problems defined on an infinite interval. In particular, we show how…
Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational…
The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. EVT supports using semi-parametric models called max-stable distributions…
Traditional RL algorithms like Proximal Policy Optimization (PPO) typically train on the entire rollout buffer, operating under the assumption that all generated episodes provide a beneficial optimization signal. However, these episodes…
Interpretability and stability are two important features that are desired in many contemporary big data applications arising in economics and finance. While the former is enjoyed to some extent by many existing forecasting approaches, the…
The scores of distance-based outlier detection methods are difficult to interpret, making it challenging to determine a cut-off threshold between normal and outlier data points without additional context. We describe a generic…
Suppose that $X_1,X_2,\ldots$ are a stream of independent, identically distributed Poisson random variables with mean $\mu$. This work presents a new estimate $\mu_k$ for $\mu$ with the property that the distribution of the relative error…
In this article, we propose a new numerical approach to high-dimensional partial differential equations (PDEs) arising in the valuation of exotic derivative securities. The proposed method is extended from Reisinger and Wittum (2007) and…