Related papers: Determinantal identity for multilevel systems and …
A coalgebraic definition of finite and infinite trace semantics for probabilistic transition systems has recently been given using a certain Kleisli category. In this paper this semantics is developed using a coalgebraic method which is an…
Given any n-tuple of complex numbers, one can canonically define a polynomial of degree n+1 that has the entries of this n-tuple as its critical points. In 2002, Beardon, Carne, and Ng studied a map $\theta\colon \mathbb{C}^n\to…
A scheme is presented to extract detailed dynamical signatures from successive measurements of complex systems. Relative entropy based time series tools are used to quantify the gain in predictive power of increasing past knowledge. By…
The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations). A new algebraically and geometrically defined system structure is…
The development of machine learning interatomic potentials faces a critical computational bottleneck with the generation and labeling of useful training datasets. We present a novel application of determinantal point processes (DPPs) to the…
There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a…
We study a mini-batch diversification scheme for stochastic gradient descent (SGD). While classical SGD relies on uniformly sampling data points to form a mini-batch, we propose a non-uniform sampling scheme based on the Determinantal Point…
A linear map between two vector spaces has a very important characteristic: a determinant. In modern theory two generalizations of linear maps are intensively used: to linear complexes (the nilpotent chains of linear maps) and to non-linear…
Determinantal points processes are a promising but relatively under-developed tool in machine learning and statistical modelling, being the canonical statistical example of distributions with repulsion. While their mathematical formulation…
It is known that determinantal point processes have an intimate relation to operator algebras. In the paper, we extend this relationship to encompass dynamical aspects. Especially, we delve into two types of determinantal point processes.…
In this paper we introduce a novel family of decision lists consisting of highly interpretable models which can be learned efficiently in a greedy manner. The defining property is that all rules are oriented in the same direction.…
Determinantal point processes (DPPs) are an elegant model for encoding probabilities over subsets, such as shopping baskets, of a ground set, such as an item catalog. They are useful for a number of machine learning tasks, including product…
Existing MAP inference algorithms for determinantal point processes (DPPs) need to calculate determinants or conduct eigenvalue decomposition generally at the scale of the full kernel, which presents a great challenge for real-world…
This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable…
In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for…
In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
Discrete diffusion models are promising alternatives to autoregressive approaches for text generation, yet their decoding methods remain under-studied. Standard decoding methods for autoregressive models, such as beam search, do not…
We aim to select data subsets for the fine-tuning of large language models to more effectively follow instructions. Prior work has emphasized the importance of diversity in dataset curation but relied on heuristics such as the number of…
We study determinantal point processes (DPP) through the lens of algebraic statistics. We count the critical points of the log-likelihood function, and we compute them for small models, thereby disproving a conjecture of Brunel, Moitra,…