Related papers: Remembering Leo Breiman
I do not remember when was the first time that I met Leo, but I have a clear memory of going to Leo's office on the 4th floor of Evans Hall to talk to him in my second year in Berkeley's Ph.D. program in 1986. The details of the…
Thomas Milton Liggett was a world renowned UCLA probabilist, famous for his monograph Interacting Particle Systems. He passed away peacefully on May 12, 2020. This is a perspective article in memory of both Tom Liggett the person and Tom…
State of the art large language models (LLMs) have shown impressive performance on a variety of benchmark tasks and are increasingly used as components in larger applications, where LLM-based predictions serve as proxies for human…
In this paper we present an effective method for computing certain real coefficients $\lambda_{n}$ which appear in a criterion for the Riemann hypothesis proved by Xian-Jin Li. With the use of this method a sequence of over three-thousand…
When estimating a regression model, we might have data where some labels are missing, or our data might be biased by a selection mechanism. When the response or selection mechanism is ignorable (i.e., independent of the response variable…
The finite sensitivity of instruments or detection methods means that data sets in many areas of astronomy, for example cosmological or exoplanet surveys, are necessarily systematically incomplete. Such data sets, where the population being…
Evidence of an algebraic/analytic structure of the Riemann Spectrum, consisting of the imaginary parts of the corresponding zeros, is reviewed, with emphasis on the distribution of the image of the primes under the Cramer characters…
In this tribute to Neil Sloane, we revisit the first sequence in the On-Line Encyclopedia of Integer Sequences, sequence A435 (1, 8, 78, 944, 13800, 237432, 4708144, 105822432, ...), that he encountered when he was a graduate student, and…
This texts commemorates the memory of Haim Brezis and explores some aspects of the restriction problem, particularly its connections to spectral and geometric analysis. Our choice of subject is motivated by Brezis' significant contributions…
This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…
The notion of two-numbers of connected Riemannian manifolds was introduced about 35 years ago in [Un invariant geometrique riemannien, C. R. Acad. Sci. Paris Math. 295 (1982), 389--391] by B.-Y. Chen and T. Nagano. Later, two-numbers have…
In "Embers of Autoregression" (McCoy et al., 2023), we showed that several large language models (LLMs) have some important limitations that are attributable to their origins in next-word prediction. Here we investigate whether these issues…
The authors are doing the readers of Statistical Science a true service with a well-written and up-to-date overview of boosting that originated with the seminal algorithms of Freund and Schapire. Equally, we are grateful for high-level…
Following the critical review of Seaman et al. (2012), we reflect on what is presumably the most essential aspect of Bayesian statistics, namely the selection of a prior density. In some cases, Bayesian inference remains fairly stable under…
We argue here about the relevance and the ultimate unity of the Bayesian approach in a neutral and agnostic manner. Our main theme is that Bayesian data analysis is an effective tool for handling complex models, as proven by the increasing…
The paper introduces scaled Bregman distances of probability distributions which admit non-uniform contributions of observed events. They are introduced in a general form covering not only the distances of discrete and continuous stochastic…
Neyman[106]'s seminal work in 1923 has been a milestone in statistics over the century, which has motivated many fundamental statistical concepts and methodology. In this review, we delve into Neyman[106]'s groundbreaking contribution and…
This is a tutorial and survey paper on Boltzmann Machine (BM), Restricted Boltzmann Machine (RBM), and Deep Belief Network (DBN). We start with the required background on probabilistic graphical models, Markov random field, Gibbs sampling,…
Structure learning of Bayesian networks is an important problem that arises in numerous machine learning applications. In this work, we present a novel approach for learning the structure of Bayesian networks using the solution of an…
Blockwise missing data occurs frequently when we integrate multisource or multimodality data where different sources or modalities contain complementary information. In this paper, we consider a high-dimensional linear regression model with…