It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the data, hence the complexity of the dataset at hand. A great variety of dimension estimators have been developed to find the intrinsic dimension of the data but there is little guidance on how to reliably use these estimators. This survey reviews a wide range of dimension estimation methods, categorising them by the geometric information they exploit: tangential estimators which detect a local affine structure; parametric estimators which rely on dimension-dependent probability distributions; and estimators which use topological or metric invariants. The paper evaluates the performance of these methods, as well as investigating varying responses to curvature and noise. Key issues addressed include robustness to hyperparameter selection, sample size requirements, accuracy in high dimensions, precision, and performance on non-linear geometries. In identifying the best hyperparameters for benchmark datasets, overfitting is frequent, indicating that many estimators may not generalise well beyond the datasets on which they have been tested.

Due to the computational complexity of evaluating interatomic forces from first principles, the creation of interatomic machine learning force fields has become a highly active field of research. However, the generation of training datasets of sufficient size and sample diversity itself comes with a computational burden that can make this approach impractical for modeling rare events or systems with a large configuration space. Fine-tuning foundation models that have been pre-trained on large-scale material or molecular databases offers a promising opportunity to reduce the amount of training data necessary to reach a desired level of accuracy. However, even if this approach requires less training data overall, creating a suitable training dataset can still be a very challenging problem, especially for systems with rare events and for end-users who don't have an extensive background in machine learning. In on-the-fly learning, the creation of a training dataset can be largely automated by using model uncertainty during the simulation to decide if the model is accurate enough or if a structure should be recalculated with classical methods and used to update the model. A key challenge for applying this form of active learning to the fine-tuning of foundation models is how to assess the uncertainty of those models during the fine-tuning process, even though most foundation models lack any form of uncertainty quantification. In this paper, we overcome this challenge by introducing a fine-tuning approach based on Bayesian neural network methods and a subsequent on-the-fly workflow that automatically fine-tunes the model while maintaining a pre-specified accuracy and can detect rare events such as transition states and sample them at an increased rate relative to their occurrence.

--Short text clustering has become increasingly important with the popularity of social media like Twitter, Google+, and Facebook. Existing methods can be broadly categorized into two paradigms: topic model-based approaches and deep representation learning-based approaches. This task is inherently challenging due to the sparse, large-scale, and high-dimensional characteristics of the short text data. Furthermore, the computational intensity required by representation learning significantly increases the running time. T o address these issues, we propose a collapsed Gibbs Sampling algorithm for the Dirichlet Multinomial Mixture model (GSDMM), which effectively handles the sparsity and high dimensionality of short texts while identifying representative words for each cluster . Based on several aspects of GSDMM that warrant further refinement, we propose an improved approach, GSDMM+, designed to further optimize its performance. GSDMM+ reduces initialization noise and adap-tively adjusts word weights based on entropy, achieving fine-grained clustering that reveals more topic-related information. Additionally, strategic cluster merging is employed to refine clustering granularity, better aligning the predicted distribution with the true category distribution. We conduct extensive experiments, comparing our methods with both classical and state-of-the-art approaches. The experimental results demonstrate the efficiency and effectiveness of our methods. The source code for our model is publicly available at https://github.com/chehaoa/VEMC. HE proliferation of mobile internet has led to an exponential increase in user-generated data on online platforms, including video, text, and image data. Intelligent processing of such data can significantly enhance the quality of life across society and generate substantial economic benefits. Short text data are a prevalent and important form of user-generated data, consisting of concise texts such as microblogs and comments.

When faced with novel situations, people are able to marshal relevant considerations from a wide range of background knowledge and put these to use in inferences and predictions. What permits us to draw in globally relevant information and reason over it coherently? Here, we explore the hypothesis that people use a combination of distributed and symbolic representations to construct bespoke mental models tailored to novel situations. We propose a computational implementation of this idea -- a ``Model Synthesis Architecture'' (MSA) -- using language models to implement global relevance-based retrieval and model synthesis and probabilistic programs to implement bespoke, coherent world models. We evaluate our MSA as a model of human judgments on a novel reasoning dataset. The dataset -- built around a `Model Olympics` domain of sports vignettes -- tests models' capacity for human-like, open-ended reasoning by requiring (i) judgments about novel causal structures described in language; (ii) drawing on large bodies of background knowledge; and (iii) doing both in light of observations that introduce arbitrary novel variables. Our MSA approach captures human judgments better than language model-only baselines, under both direct and chain-of-thought generations from the LM that supports model synthesis. These results suggest that MSAs can be implemented in a way that mirrors people's ability to deliver locally coherent reasoning over globally relevant variables, offering a path to understanding and replicating human reasoning in open-ended domains.

In modern applications, these models typically involve a large number of parameters and latent variables, resulting in complex and high-dimensional posteriors that are computationally intractable. For such scenarios, traditional Markov chain Monte Carlo (MCMC) approaches often suffer from lengthy burn-in periods and generally lack scalability [11]. Recently, variational inference (VI) [31, 10, 52, 11] has emerged as a popular and scalable alternative method for approximating intractable posterior distributions in large-scale applications (where the number of observations and dimensionality are both large) and is typically orders of magnitude faster than MCMC methods. Among the various forms of VI, arguably the most widely used and important is mean-field variational inference (MFVI) [52, 11], which approximates the intractable posterior by a product distribution. This approach has been widely adopted in statistics and machine learning, thanks to efficient algorithmic implementations based on coordinate ascent variational inference (CAVI) [10, 11, 19, 7, 5, 36, 14, 34].

Predicting a response with partially missing inputs remains a challenging task even in parametric models, since parameter estimation in itself is not sufficient to predict on partially observed inputs. Several works study prediction in linear models. In this paper, we focus on logistic models, which present their own difficulties. From a theoretical perspective, we prove that a Pattern-by-Pattern strategy (PbP), which learns one logistic model per missingness pattern, accurately approximates Bayes probabilities in various missing data scenarios (MCAR, MAR and MNAR). Empirically, we thoroughly compare various methods (constant and iterative imputations, complete case analysis, PbP, and an EM algorithm) across classification, probability estimation, calibration, and parameter inference. Our analysis provides a comprehensive view on the logistic regression with missing values. It reveals that mean imputation can be used as baseline for low sample sizes, and improved performance is obtained via nonlinear multiple iterative imputation techniques with the labels ( MICE.RF.Y). For large sample sizes, PbP is the best method for Gaussian mixtures, and we recommend MICE.RF.Y in presence of nonlinear features.

The identification of Linear Time-V ariant (L TV) systems from input-output data is a fundamental yet challenging ill-posed inverse problem. This work introduces a unified Bayesian framework that models the system's impulse response, h( t,τ), as a stochastic process. We decompose the response into a posterior mean and a random fluctuation term, a formulation that provides a principled approach for quantifying uncertainty and naturally defines a new, useful system class we term Linear Time-Invariant in Expectation (L TIE). To perform inference, we leverage modern machine learning techniques, including Bayesian neural networks and Gaussian Processes, using scalable variational inference. We demonstrate through a series of experiments that our framework can robustly infer the properties of an L TI system from a single noisy observation, show superior data e fficiency compared to classical methods in a simulated ambient noise tomography problem, and successfully track a continuously varying L TV impulse response by using a structured Gaussian Process prior. This work provides a flexible and robust methodology for uncertainty-aware system identification in dynamic environments.1. Introduction Linear Time-V ariant (L TV) systems are fundamental to modeling dynamic processes in fields ranging from geophysics and communications to control theory (Kozachek et al., 2024; Lin et al., 2020). Unlike their time-invariant counterparts, an L TV system's behavior is described by an impulse response, h( t,τ), that changes over time, posing significant challenges for analysis and estimation (Kailath, 1962; Bello, 1963). The task of identifying h( t,τ) from input-output data is a severely ill-posed inverse problem, as one must infer a function of two variables from one-dimensional time series (Aubel and B olcskei, 2015). This work introduces a Bayesian framework for modeling such systems, where the inherent uncertainty and time-varying nature are captured probabilistically.

Symbolic regression is the machine learning method for learning functions from data. After a brief overview of the symbolic regression landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown (and likely significant) probability of failing to find any given good function, and they suffer from ambiguity and poorly-justified assumptions in their function-selection procedure. To address these I propose an exhaustive search and model selection by the minimum description length principle, which allows accuracy and complexity to be directly traded off by measuring each in units of information. I showcase the resulting publicly available Exhaustive Symbolic Regression algorithm on three open problems in astrophysics: the expansion history of the universe, the effective behaviour of gravity in galaxies and the potential of the inflaton field. In each case the algorithm identifies many functions superior to the literature standards. This general purpose methodology should find widespread utility in science and beyond.

Probabilistic Event Calculus (PEC) is a logical framework for reasoning about actions and their effects in uncertain environments, which enables the representation of probabilistic narratives and computation of temporal projections. The PEC formalism offers significant advantages in interpretability and expressiveness for narrative reasoning. However, it lacks mechanisms for goal-directed reasoning. This paper bridges this gap by developing a formal translation of PEC domains into Markov Decision Processes (MDPs), introducing the concept of "action-taking situations" to preserve PEC's flexible action semantics. The resulting PEC-MDP formalism enables the extensive collection of algorithms and theoretical tools developed for MDPs to be applied to PEC's interpretable narrative domains. We demonstrate how the translation supports both temporal reasoning tasks and objective-driven planning, with methods for mapping learned policies back into human-readable PEC representations, maintaining interpretability while extending PEC's capabilities.

An increasing number of applications are exploiting sampling-based algorithms for planning, optimization, and inference. The Markov Chain Monte Carlo (MCMC) algorithms form the computational backbone of this emerging branch of machine learning. Unfortunately, the high computational cost limits their feasibility for large-scale problems and real-world applications, and the existing MCMC acceleration solutions are either limited in hardware flexibility or fail to maintain efficiency at the system level across a variety of end-to-end applications. This paper introduces \textbf{MC$^2$A}, an algorithm-hardware co-design framework, enabling efficient and flexible optimization for MCMC acceleration. Firstly, \textbf{MC$^2$A} analyzes the MCMC workload diversity through an extension of the processor performance roofline model with a 3rd dimension to derive the optimal balance between the compute, sampling and memory parameters. Secondly, \textbf{MC$^2$A} proposes a parametrized hardware accelerator architecture with flexible and efficient support of MCMC kernels with a pipeline of ISA-programmable tree-structured processing units, reconfigurable samplers and a crossbar interconnect to support irregular access. Thirdly, the core of \textbf{MC$^2$A} is powered by a novel Gumbel sampler that eliminates exponential and normalization operations. In the end-to-end case study, \textbf{MC$^2$A} achieves an overall {$307.6\times$, $1.4\times$, $2.0\times$, $84.2\times$} speedup compared to the CPU, GPU, TPU and state-of-the-art MCMC accelerator. Evaluated on various representative MCMC workloads, this work demonstrates and exploits the feasibility of general hardware acceleration to popularize MCMC-based solutions in diverse application domains.