The Kalman filter and Rauch-Tung-Striebel (RTS) smoother are optimal for state estimation in linear dynamic systems. With nonlinear systems, the challenge consists in how to propagate uncertainty through the state transitions and output function. For the case of a neural network model, we enable accurate uncertainty propagation using a recent state-of-the-art analytic formula for computing the mean and covariance of a deep neural network with Gaussian input. We argue that cross entropy is a more appropriate performance metric than RMSE for evaluating the accuracy of filters and smoothers. We demonstrate the superiority of our method for state estimation on a stochastic Lorenz system and a Wiener system, and find that our method enables more optimal linear quadratic regulation when the state estimate is used for feedback.

Establishing a communication system is hard because the intended meaning of a signal is unknown to its receiver when first produced, and the signaller also has no idea how that signal will be interpreted. Most theoretical accounts of the emergence of communication systems rely on feedback to reinforce behaviours that have led to successful communication in the past. However, providing such feedback requires already being able to communicate the meaning that was intended or interpreted. Therefore these accounts cannot explain how communication can be bootstrapped from non-communicative behaviours. Here we present a model that shows how a communication system, capable of expressing an unbounded number of meanings, can emerge as a result of individual behavioural differences in a large population without any pre-existing means to determine communicative success. The two key cognitive capabilities responsible for this outcome are behaving predictably in a given situation, and an alignment of psychological states ahead of signal production that derives from shared intentionality. Since both capabilities can exist independently of communication, our results are compatible with theories in which large flexible socially-learned communication systems like language are the product of a general but well-developed capacity for social cognition.

Physics-informed deep learning has emerged as a promising framework for solving partial differential equations (PDEs). Nevertheless, training these models on complex problems remains challenging, often leading to limited accuracy and efficiency. In this work, we introduce a hybrid adaptive sampling and weighting method to enhance the performance of physics-informed neural networks (PINNs). The adaptive sampling component identifies training points in regions where the solution exhibits rapid variation, while the adaptive weighting component balances the convergence rate across training points. Numerical experiments show that applying only adaptive sampling or only adaptive weighting is insufficient to consistently achieve accurate predictions, particularly when training points are scarce. Since each method emphasizes different aspects of the solution, their effectiveness is problem dependent. By combining both strategies, the proposed framework consistently improves prediction accuracy and training efficiency, offering a more robust approach for solving PDEs with PINNs.

Tree-based methods are a family of non-parametric approaches in supervised learning. Random forests use a form of bootstrap aggregation, or bagging, to combine a large collection of trees and produce a final prediction. In regression problems, it gives the same weight to each tree and computes the average out-of-bag prediction. In classification problems, it assigns class labels by majority vote. However, since a single-tree model is known to have high variance, a large number of trees need to be trained and aggregated in order to reduce variance (Hastie et al. 2009). This can lead to redundant trees, as the bootstrap procedure may select similar sets of samples to train different trees. Moreover, increasing the number of trees does not reduce the bias. Post-selection boosting random forests, proposed by Wang & Wang (2021), is an attempt to reduce bias by applying Lasso regression (Tibshirani 1996) on the predictions from each individual tree. The method returns a sparser forest with fewer trees, as well as different weights assigned to each individual tree.

The ubiquitous nature of mobile health (mHealth) technology has expanded opportunities for the integration of reinforcement learning into traditional clinical trial designs, allowing researchers to learn individualized treatment policies during the study. LowSalt4Life 2 (LS4L2) is a recent trial aimed at reducing sodium intake among hypertensive individuals through an app-based intervention. A reinforcement learning algorithm, which was deployed in one of the trial arms, was designed to send reminder notifications to promote app engagement in contexts where the notification would be effective, i.e., when a participant is likely to open the app in the next 30-minute and not when prior data suggested reduced effectiveness. Such an algorithm can improve app-based mHealth interventions by reducing participant burden and more effectively promoting behavior change. We encountered various challenges during the implementation of the learning algorithm, which we present as a template to solving challenges in future trials that deploy reinforcement learning algorithms. We provide template solutions based on LS4L2 for solving the key challenges of (i) defining a relevant reward, (ii) determining a meaningful timescale for optimization, (iii) specifying a robust statistical model that allows for automation, (iv) balancing model flexibility with computational cost, and (v) addressing missing values in gradually collected data.

Leslie Valiant's 1984 paper "A Theory of the Learnable" [Val84], reproduced in this volume, has the unusual distinction of having changed the course of several scientific disciplines. Within theoretical computer science it was one of the key works giving rise to the field now known as computational learning theory, which may loosely be defined as the rigorous study of learning processes and phenomena from the computer science perspective of efficient algorithms and computational complexity. In the decades since the publication of [Val84], computational learning theory has grown into a rich field with strong connections to many other theoretical disciplines such as mathematical probability and statistics, information theory, decision theory and more. Beyond the realm of theory, Valiant's paper and the Probably Approximately Correct (PAC) model which he introduced in it have also had a great impact on the subsequent development of machine learning, a field which has already transformed many aspects of science and human society and seems certain to have an even greater influence in the future. This chapter gives an overview of the Probably Approximately Correct learning model that Valiant introduced in [Val84], explaining some of the major results and directions that the field has taken in the years since that work.

Machine learning (ML) classification models are increasingly being used in a wide range of applications where it is important that predictions are accompanied by uncertainties, including in climate and earth observation, medical diagnosis and bioaerosol monitoring. The output of an ML classification model is a type of categorical variable known as a nominal property in the International Vocabulary of Metrology (VIM). However, concepts related to uncertainty evaluation for nominal properties are not defined in the VIM, nor is such evaluation addressed by the Guide to the Expression of Uncertainty in Measurement (GUM). In this paper we propose a metrological conceptual uncertainty evaluation framework for nominal properties. This framework is based on probability mass functions and summary statistics thereof, and it is applicable to ML classification. We also illustrate its use in the context of two applications that exemplify the issues and have significant societal impact, namely, climate and earth observation and medical diagnosis. Our framework would enable an extension of the GUM to uncertainty for nominal properties, which would make both applicable to ML classification models.

Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based on local neighbourhood structures and require tuning the number of neighbours that define this local structure, and the dimensionality of the lower-dimensional space onto which the data are projected. Such choices critically influence the quality of the resulting embedding. In this paper, we exploit a recently proposed intrinsic dimension estimator which also returns the optimal locally adaptive neighbourhood sizes according to some desirable criteria. In principle, this adaptive framework can be employed to perform an optimal hyper-parameter tuning of any dimensionality reduction algorithm that relies on local neighbourhood structures. Numerical experiments on both real-world and simulated datasets show that the proposed method can be used to significantly improve well-known projection methods when employed for various learning tasks, with improvements measurable through both quantitative metrics and the quality of low-dimensional visualizations.

Large language models have shown remarkable language processing and reasoning ability but are prone to hallucinate when asked about private data. Retrieval-augmented generation (RAG) retrieves relevant data that fit into an LLM's context window and prompts the LLM for an answer. GraphRAG extends this approach to structured Knowledge Graphs (KGs) and questions regarding entities multiple hops away. The majority of recent GraphRAG methods either overlook the retrieval step or have ad hoc retrieval processes that are abstract or inefficient. This prevents them from being adopted when the KGs are stored in graph databases supporting graph query languages. In this work, we present GraphRAFT, a retrieve-and-reason framework that finetunes LLMs to generate provably correct Cypher queries to retrieve high-quality subgraph contexts and produce accurate answers. Our method is the first such solution that can be taken off-the-shelf and used on KGs stored in native graph DBs. Benchmarks suggest that our method is sample-efficient and scales with the availability of training data. Our method achieves significantly better results than all state-of-the-art models across all four standard metrics on two challenging Q&As on large text-attributed KGs.

The advancements in systems deploying large language models (LLMs), as well as improvements in their ability to act as agents with predefined templates, provide an opportunity to conduct qualitative, individualized assessments, creating a bridge between qualitative and quantitative methods for candidates seeking career progression. In this paper, we develop a platform that allows candidates to run AI-led interviews to assess their current career stage and curate coursework to enable progression to the next level. Our approach incorporates predefined career trajectories, associated skills, and a method to recommend the best resources for gaining the necessary skills for advancement. We employ OpenAI API calls along with expertly compiled chat templates to assess candidate competence. Our platform is highly configurable due to the modularity of the development, is easy to deploy and use, and available as a web interface where the only requirement is candidate resumes in PDF format. We demonstrate a use-case centered on software engineering and intend to extend this platform to be domain-agnostic, requiring only regular updates to chat templates as industries evolve.