相关论文: LP Approach to Statistical Modeling

Machine learning (ML) is playing an increasingly important role in scientific research. In conjunction with classical statistical approaches, ML-assisted analytical strategies have shown great promise in accelerating research findings. This…

Linguistic typology aims to capture structural and semantic variation across the world's languages. A large-scale typology could provide excellent guidance for multilingual Natural Language Processing (NLP), particularly for languages that…

This paper addresses classification problems with matrix-valued data, which commonly arise in applications such as neuroimaging and signal processing. Building on the assumption that the data from each class follows a matrix normal…

In recent years, the field of statistics has experienced a surge in interest and application, largely due to significant advances in computer technology. This progress has led to remarkable developments in statistics methods and algorithms,…

Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…

The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…

A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the…

Key to structured prediction is exploiting the problem structure to simplify the learning process. A major challenge arises when data exhibit a local structure (e.g., are made by "parts") that can be leveraged to better approximate the…

A common approach to synthetic data is to sample from a fitted model. We show that under general assumptions, this approach results in a sample with inefficient estimators and whose joint distribution is inconsistent with the true…

Mathematical models are vital to the field of metrology, playing a key role in the derivation of measurement results and the calculation of uncertainties from measurement data, informed by an understanding of the measurement process. These…

We introduce a novel approach to compositional data analysis based on $L^{\infty}$-normalization, addressing challenges posed by zero-rich high-throughput data. Traditional methods like Aitchison's transformations require excluding zeros,…

This paper discusses a method for implementing a probabilistic inference system based on an extended relational data model. This model provides a unified approach for a variety of applications such as dynamic programming, solving sparse…

The history of data analysis that is addressed here is underpinned by two themes, -- those of tabular data analysis, and the analysis of collected heterogeneous data. "Exploratory data analysis" is taken as the heuristic approach that…

Measurement is a fundamental building block of numerous scientific models and their creation. This is in particular true for data driven science. Due to the high complexity and size of modern data sets, the necessity for the development of…

We present a method to integrate Large Language Models (LLMs) and traditional tabular data classification techniques, addressing LLMs challenges like data serialization sensitivity and biases. We introduce two strategies utilizing LLMs for…

This work in progress aims to provide a unified introduction to statistical learning, building up slowly from classical models like the GMM and HMM to modern neural networks like the VAE and diffusion models. There are today many internet…

We propose a new method for modelling simple longitudinal data. We aim to do this in a flexible manner (without restrictive assumptions about the shapes of individual trajectories), while exploiting structural similarities between the…

Ranking data represent a peculiar form of multivariate ordinal data taking values in the set of permutations. Despite the numerous methodological contributions to increase the flexibility of ranked data modeling, the application of more…

Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…

In modern spatial statistics, the structure of data that is collected has become more heterogeneous. Depending on the type of spatial data, different modeling strategies for spatial data are used. For example, a kriging approach for…