Deconvolution problems arise in a variety of situations in statistics. An interesting problem is to estimate the density $f$ of a random variable $X$ based on $n$ i.i.d. observations from $Y = X + \varepsilon$, where $\varepsilon$ is a measurement error with a known distribution.…
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The history of mathematical statistics in the United States prior to 1885 is reviewed, with emphasis upon the works of Robert Adrain, Benjamin and Charles Peirce, Simon Newcomb, and Erastus De Forest. While the period before 1850 produced little of substance, the years from 1850…
Pretraining Large Language Models (LLMs) on large corpora of textual data is now a standard paradigm. When using these LLMs for many downstream applications, it is common to additionally bake in new knowledge (e.g., time-critical news, or private domain knowledge) into the pretra…
up optimality in Wiktionary, the free dictionary. Optimality may refer to: Mathematical optimization Optimality theory in linguistics Optimality model
research Opinion poll Optimal decision Optimal design Optimal discriminant analysis Optimal matching Optimal stopping Optimality criterion Optimistic knowledge
optimal meaning, definition, what is optimal: the best or most suitable: Learn more.
We present a novel method for solving a class of time-inconsistent optimal stopping problems by reducing them to a family of standard stochastic optimal control problems. In particular, we convert an optimal stopping problem with a non-linear functio...
We investigate the estimation of an optimal transport map between probability measures on an infinite-dimensional space and reveal its minimax optimal rate. Optimal transport theory defines distances within a space of probability measures, utilizing...
Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans $π_1, π_2, \ldots$ converges weakly to a transport plan $π$, then $π$ is also optimal (between its marginals). A...
Reinforcement Learning has drawn huge interest as a tool for solving optimal control problems. Solving a given problem (task or environment) involves converging towards an optimal policy. However, there might exist multiple optimal policies that can...
The home space for optimal control is a Sobolev space. The home space for pseudospectral theory is also a Sobolev space. It thus seems natural to combine pseudospectral theory with optimal control theory and construct ``pseudospectral optimal control...
Optimal experimental design approaches are seldom used in pre-clinical drug discovery. Main reasons for this lack of use are that available software tools require relatively high insight in optimal design theory, and that the design-execution cycle o...
We analyze an optimal stopping problem with a series of inequality-type and equality-type expectation constraints in a general non-Markovian framework. We show that the optimal stopping problem with expectation constraints (OSEC) in an arbitrary prob...
We study the optimal cloning transformation for two pairs of orthogonal states of two-dimensional quantum systems, and derive the corresponding optimal fidelities....
While the scaling laws of large language models (LLMs) training have been extensively studied, optimal inference configurations of LLMs remain underexplored. We study inference scaling laws (aka test-time scaling laws) and compute-optimal inference,...
In this paper we shall consider optimal scaling problems for high-dimensional Metropolis--Hastings algorithms where updates can be chosen to be lower dimensional than the target density itself. We find that the optimal scaling rule for the Metropol...
The problem of finding the optimal tapering of a free (non-supported) javelin is described and solved. For the optimal javelin, the lowest mode of vibration has the highest possible frequency. With this tapering inner damping will lead to the cessa...
We introduce locality: a new property of multi-bidder auctions that formally separates the simplicity of optimal single-dimensional multi-bidder auctions from the complexity of optimal multi-dimensional multi-bidder auctions. Specifically, consider t...