Related papers: On the " Froissaron-Maximal Odderon" Model

This paper presents some results on the maximum likelihood (ML) estimation from incomplete data. Finite sample properties of conditional observed information matrices are established. They possess positive definiteness and the same Loewner…

A set of general formulas is proposed for the probability of failure on demand (PFD) assessment of MooN architecture (i.e. k-out-of-n) systems subject to partial and full tests. Partial tests (e.g. visual inspections, imperfect testing) may…

Let $\mathcal{F}=\{F_1,F_2, \ldots,F_n\}$ be a family of $n$ sets on a ground set $S$, such as a family of balls in $\mathbb{R}^d$. For every finite measure $\mu$ on $S$, such that the sets of $\mathcal{F}$ are measurable, the classical…

Misleading or unnecessary data can have out-sized impacts on the health or accuracy of Machine Learning (ML) models. We present a Bayesian sequential selection method, akin to Bayesian experimental design, that identifies critically…

The F-measure, which has originally been introduced in information retrieval, is nowadays routinely used as a performance metric for problems such as binary classification, multi-label classification, and structured output prediction.…

The advent of large-scale inference has spurred reexamination of conventional statistical thinking. In a Gaussian model for $n$ many $z$-scores with at most $k < \frac{n}{2}$ nonnulls, Efron suggests estimating the location and scale…

Although G\"odel's incompleteness theorem made mathematician recognize that no axiomatic system could completely prove its correctness and that there is an eternal hole between our knowledge and the world, physicists so far continue to work…

When constructing models of the world, we aim for optimal compressions: models that include as few details as possible while remaining as accurate as possible. But which details -- or features measured in data -- should we choose to include…

The mathematical models used to represent physical phenomena are generally known to be imperfect representations of reality. Model inadequacies arise for numerous reasons, such as incomplete knowledge of the phenomena or computational…

Multimodal data collected from the real world are often imperfect due to missing modalities. Therefore multimodal models that are robust against modal-incomplete data are highly preferred. Recently, Transformer models have shown great…

The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably…

This paper provides further insight into the key concept of missing at random (MAR) in incomplete data analysis. Following the usual selection modelling approach we envisage two models with separable parameters: a model for the response of…

We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in…

Factorization machine (FM) is a popular machine learning model to capture the second order feature interactions. The optimal learning guarantee of FM and its generalized version is not yet developed. For a rank $k$ generalized FM of $d$…

Frontier AI models demonstrate formidable breadth of knowledge. But how close are they to true human -- or superhuman -- expertise? Genuine experts can tackle the hardest problems and push the boundaries of scientific understanding. To…

Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients,…

In Positron Emission Tomography, movement leads to blurry reconstructions when not accounted for. Whether known a priori or estimated jointly to reconstruction, motion models are increasingly defined in continuum rather that in discrete,…

Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…

Ideally, all analyses of normally distributed data should include the full covariance information between all data points. In practice, the full covariance matrix between all data points is not always available. Either because a result was…

We propose a statistically optimal approach to construct data-driven decisions for stochastic optimization problems. Fundamentally, a data-driven decision is simply a function that maps the available training data to a feasible action. It…