Agent-based modeling has been around for decades, and applied widely across the social and natural sciences. The scope of this research method is now poised to grow dramatically as it absorbs the new affordances provided by Large Language Models (LLM)s. Generative Agent-Based Models (GABM) are not just classic Agent-Based Models (ABM)s where the agents talk to one another. Rather, GABMs are constructed using an LLM to apply common sense to situations, act "reasonably", recall common semantic knowledge, produce API calls to control digital technologies like apps, and communicate both within the simulation and to researchers viewing it from the outside. Here we present Concordia, a library to facilitate constructing and working with GABMs. Concordia makes it easy to construct language-mediated simulations of physically- or digitally-grounded environments. Concordia agents produce their behavior using a flexible component system which mediates between two fundamental operations: LLM calls and associative memory retrieval. A special agent called the Game Master (GM), which was inspired by tabletop role-playing games, is responsible for simulating the environment where the agents interact. Agents take actions by describing what they want to do in natural language. The GM then translates their actions into appropriate implementations. In a simulated physical world, the GM checks the physical plausibility of agent actions and describes their effects. In digital environments simulating technologies such as apps and services, the GM may handle API calls to integrate with external tools such as general AI assistants (e.g., Bard, ChatGPT), and digital apps (e.g., Calendar, Email, Search, etc.). Concordia was designed to support a wide array of applications both in scientific research and for evaluating performance of real digital services by simulating users and/or generating synthetic data.
Modern machine learning applications have witnessed the remarkable success of optimization algorithms that are designed to find flat minima. Motivated by this design choice, we undertake a formal study that (i) formulates the notion of flat minima, and (ii) studies the complexity of finding them. Specifically, we adopt the trace of the Hessian of the cost function as a measure of flatness, and use it to formally define the notion of approximate flat minima. Under this notion, we then analyze algorithms that find approximate flat minima efficiently. For general cost functions, we discuss a gradient-based algorithm that finds an approximate flat local minimum efficiently. The main component of the algorithm is to use gradients computed from randomly perturbed iterates to estimate a direction that leads to flatter minima. For the setting where the cost function is an empirical risk over training data, we present a faster algorithm that is inspired by a recently proposed practical algorithm called sharpness-aware minimization, supporting its success in practice.
Generative diffusion models and many stochastic models in science and engineering naturally live in infinite dimensions before discretisation. To incorporate observed data for statistical and learning tasks, one needs to condition on observations. While recent work has treated conditioning linear processes in infinite dimensions, conditioning non-linear processes in infinite dimensions has not been explored. This paper conditions function valued stochastic processes without prior discretisation. To do so, we use an infinite-dimensional version of Girsanov's theorem to condition a function-valued stochastic process, leading to a stochastic differential equation (SDE) for the conditioned process involving the score. We apply this technique to do time series analysis for shapes of organisms in evolutionary biology, where we discretise via the Fourier basis and then learn the coefficients of the score function with score matching methods.
Approximation of high dimensional functions is in the focus of machine learning and data-based scientific computing. In many applications, empirical risk minimisation techniques over nonlinear model classes are employed. Neural networks, kernel methods and tensor decomposition techniques are among the most popular model classes. We provide a numerical study comparing the performance of these methods on various high-dimensional functions with focus on optimal control problems, where the collection of the dataset is based on the application of the State-Dependent Riccati Equation.
The problem of estimating a parameter in the drift coefficient is addressed for $N$ discretely observed independent and identically distributed stochastic differential equations (SDEs). This is done considering additional constraints, wherein only public data can be published and used for inference. The concept of local differential privacy (LDP) is formally introduced for a system of stochastic differential equations. The objective is to estimate the drift parameter by proposing a contrast function based on a pseudo-likelihood approach. A suitably scaled Laplace noise is incorporated to meet the privacy requirements. Our key findings encompass the derivation of explicit conditions tied to the privacy level. Under these conditions, we establish the consistency and asymptotic normality of the associated estimator. Notably, the convergence rate is intricately linked to the privacy level, and is some situations may be completely different from the case where privacy constraints are ignored. Our results hold true as the discretization step approaches zero and the number of processes $N$ tends to infinity.
SDRDPy is a desktop application that allows experts an intuitive graphic and tabular representation of the knowledge extracted by any supervised descriptive rule discovery algorithm. The application is able to provide an analysis of the data showing the relevant information of the data set and the relationship between the rules, data and the quality measures associated for each rule regardless of the tool where algorithm has been executed. All of the information is presented in a user-friendly application in order to facilitate expert analysis and also the exportation of reports in different formats.
Executive functioning is a cognitive process that enables humans to plan, organize, and regulate their behavior in a goal-directed manner. Understanding and classifying the changes in executive functioning after longitudinal interventions (like transcranial direct current stimulation (tDCS)) has not been explored in the literature. This study employs functional connectivity and machine learning algorithms to classify executive functioning performance post-tDCS. Fifty subjects were divided into experimental and placebo control groups. EEG data was collected while subjects performed an executive functioning task on Day 1. The experimental group received tDCS during task training from Day 2 to Day 8, while the control group received sham tDCS. On Day 10, subjects repeated the tasks specified on Day 1. Different functional connectivity metrics were extracted from EEG data and eventually used for classifying executive functioning performance using different machine learning algorithms. Results revealed that a novel combination of partial directed coherence and multi-layer perceptron (along with recursive feature elimination) resulted in a high classification accuracy of 95.44%. We discuss the implications of our results in developing real-time neurofeedback systems for assessing and enhancing executive functioning performance post-tDCS administration.
Time series and extreme value analyses are two statistical approaches usually applied to study hydrological data. Classical techniques, such as ARIMA models (in the case of mean flow predictions), and parametric generalised extreme value (GEV) fits and nonparametric extreme value methods (in the case of extreme value theory) have been usually employed in this context. In this paper, nonparametric functional data methods are used to perform mean monthly flow predictions and extreme value analysis, which are important for flood risk management. These are powerful tools that take advantage of both, the functional nature of the data under consideration and the flexibility of nonparametric methods, providing more reliable results. Therefore, they can be useful to prevent damage caused by floods and to reduce the likelihood and/or the impact of floods in a specific location. The nonparametric functional approaches are applied to flow samples of two rivers in the U.S. In this way, monthly mean flow is predicted and flow quantiles in the extreme value framework are estimated using the proposed methods. Results show that the nonparametric functional techniques work satisfactorily, generally outperforming the behaviour of classical parametric and nonparametric estimators in both settings.
In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.
Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characterize the optimization and generalization of deep learning, partially inspired by Bayesian inference; (3) the geometrical structures of the loss landscape that drives the trajectories of the dynamic systems; (4) the roles of over-parameterization of deep neural networks from both positive and negative perspectives; (5) theoretical foundations of several special structures in network architectures; and (6) the increasingly intensive concerns in ethics and security and their relationships with generalizability.
Machine-learning models have demonstrated great success in learning complex patterns that enable them to make predictions about unobserved data. In addition to using models for prediction, the ability to interpret what a model has learned is receiving an increasing amount of attention. However, this increased focus has led to considerable confusion about the notion of interpretability. In particular, it is unclear how the wide array of proposed interpretation methods are related, and what common concepts can be used to evaluate them. We aim to address these concerns by defining interpretability in the context of machine learning and introducing the Predictive, Descriptive, Relevant (PDR) framework for discussing interpretations. The PDR framework provides three overarching desiderata for evaluation: predictive accuracy, descriptive accuracy and relevancy, with relevancy judged relative to a human audience. Moreover, to help manage the deluge of interpretation methods, we introduce a categorization of existing techniques into model-based and post-hoc categories, with sub-groups including sparsity, modularity and simulatability. To demonstrate how practitioners can use the PDR framework to evaluate and understand interpretations, we provide numerous real-world examples. These examples highlight the often under-appreciated role played by human audiences in discussions of interpretability. Finally, based on our framework, we discuss limitations of existing methods and directions for future work. We hope that this work will provide a common vocabulary that will make it easier for both practitioners and researchers to discuss and choose from the full range of interpretation methods.