Related papers: Model structures and structural identifiability: W…
Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…
A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
This paper presents a novel method for structural data recognition using a large number of graph models. In general, prevalent methods for structural data recognition have two shortcomings: 1) Only a single model is used to capture…
Sensor-driven systems are increasingly ubiquitous: they provide both data and information that can facilitate real-time decision-making and autonomous actuation, as well as enabling informed policy choices by service providers and…
How to integrate and verify spatial intelligence in foundation models remains an open challenge. Current practice often proxies Visual-Spatial Intelligence (VSI) with purely textual prompts and VQA-style scoring, which obscures geometry,…
Identifiability concerns finding which unknown parameters of a model can be estimated from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is…
A parameter of a mathematical model is structurally identifiable if it can be determined from noiseless experimental data. Here, we examine the identifiability properties of two important classes of linear compartmental models:…
Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…
Our ability to grasp and understand complex phenomena is essentially based on recognizing structures and relating these to each other. For example, any meteorological description of a weather condition and explanation of its evolution…
We show a data-driven approach to discover the underlying structural form of the mathematical equation governing the dynamics of multiple but similar systems induced by the same mechanisms. This approach hinges on theories that we lay out…
Statistical latent class models are widely used in social and psychological researches, yet it is often difficult to establish the identifiability of the model parameters. In this paper we consider the identifiability issue of a family of…
The performance of sparse matrix computation highly depends on the matching of the matrix format with the underlying structure of the data being computed on. Different sparse matrix formats are suitable for different structures of data.…
Perceptual similarity scores that align with human vision are critical for both training and evaluating computer vision models. Deep perceptual losses, such as LPIPS, achieve good alignment but rely on complex, highly non-linear…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…
Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise…
In previous work, we introduced a method for modeling a configuration of objects in 2D and 3D images using a mathematical "medial/skeletal linking structure." In this paper, we show how these structures allow us to capture positional…
Artificial General Intelligence (AGI) is closer than ever to becoming a reality, sparking widespread enthusiasm in the research community to collect and work with various modalities, including text, image, video, and audio. Despite recent…
We develop a linear response framework for interpretability that treats a neural network as a Bayesian statistical mechanical system. A small perturbation of the data distribution, for example shifting the Pile toward GitHub or legal text,…