We address the tasks of Bayesian state estimation and forecasting for a model-free process in an unsupervised learning setup. In the article, we propose DANSE -- a Data-driven Nonlinear State Estimation method. DANSE provides a closed-form posterior of the state of the model-free process, given linear measurements of the state. In addition, it provides a closed-form posterior for forecasting. A data-driven recurrent neural network (RNN) is used in DANSE to provide the parameters of a prior of the state. The prior depends on the past measurements as input, and then we find the closed-form posterior of the state using the current measurement as input. The data-driven RNN captures the underlying non-linear dynamics of the model-free process. The training of DANSE, mainly learning the parameters of the RNN, is executed using an unsupervised learning approach. In unsupervised learning, we have access to a training dataset comprising only a set of measurement data trajectories, but we do not have any access to the state trajectories. Therefore, DANSE does not have access to state information in the training data and can not use supervised learning. Using simulated linear and non-linear process models (Lorenz attractor and Chen attractor), we evaluate the unsupervised learning-based DANSE. We show that the proposed DANSE, without knowledge of the process model and without supervised learning, provides a competitive performance against model-driven methods, such as the Kalman filter (KF), extended KF (EKF), unscented KF (UKF), and a recently proposed hybrid method called KalmanNet.

Models of many real-life applications, such as queuing models of communication networks or computing systems, have a countably infinite state-space. Algorithmic and learning procedures that have been developed to produce optimal policies mainly focus on finite state settings, and do not directly apply to these models. To overcome this lacuna, in this work we study the problem of optimal control of a family of discrete-time countable state-space Markov Decision Processes (MDPs) governed by an unknown parameter $\theta\in\Theta$, and defined on a countably-infinite state space $\mathcal X=\mathbb{Z}_+^d$, with finite action space $\mathcal A$, and an unbounded cost function. We take a Bayesian perspective with the random unknown parameter $\boldsymbol{\theta}^*$ generated via a given fixed prior distribution on $\Theta$. To optimally control the unknown MDP, we propose an algorithm based on Thompson sampling with dynamically-sized episodes: at the beginning of each episode, the posterior distribution formed via Bayes' rule is used to produce a parameter estimate, which then decides the policy applied during the episode. To ensure the stability of the Markov chain obtained by following the policy chosen for each parameter, we impose ergodicity assumptions. From this condition and using the solution of the average cost Bellman equation, we establish an $\tilde O(\sqrt{|\mathcal A|T})$ upper bound on the Bayesian regret of our algorithm, where $T$ is the time-horizon. Finally, to elucidate the applicability of our algorithm, we consider two different queuing models with unknown dynamics, and show that our algorithm can be applied to develop approximately optimal control algorithms.

This paper is a submission to the Open Philanthropy AI Worldviews Contest. In it, we estimate the likelihood of transformative artificial general intelligence (AGI) by 2043 and find it to be <1%. Specifically, we argue: The bar is high: AGI as defined by the contest - something like AI that can perform nearly all valuable tasks at human cost or less - which we will call transformative AGI is a much higher bar than merely massive progress in AI, or even the unambiguous attainment of expensive superhuman AGI or cheap but uneven AGI. Many steps are needed: The probability of transformative AGI by 2043 can be decomposed as the joint probability of a number of necessary steps, which we group into categories of software, hardware, and sociopolitical factors. No step is guaranteed: For each step, we estimate a probability of success by 2043, conditional on prior steps being achieved. Many steps are quite constrained by the short timeline, and our estimates range from 16% to 95%. Therefore, the odds are low: Multiplying the cascading conditional probabilities together, we estimate that transformative AGI by 2043 is 0.4% likely. Reaching >10% seems to require probabilities that feel unreasonably high, and even 3% seems unlikely. Thoughtfully applying the cascading conditional probability approach to this question yields lower probability values than is often supposed. This framework helps enumerate the many future scenarios where humanity makes partial but incomplete progress toward transformative AGI.

Commonly used objective functions (losses) for a supervised optimization of discriminative neural network classifiers were either distribution-based or metric-based. The distribution-based losses could compromise the generalization or cause classification biases towards the dominant classes of an imbalanced class-sample distribution. The metric-based losses could make the network model independent of any distribution and thus improve its generalization. However, they could still be biased towards the dominant classes and could suffer from discrepancies when a class was absent in both the reference (ground truth) and the predicted labels. In this paper, we proposed a novel optimization process which not only tackled the unbalancedness of the class-sample distribution of the training samples but also provided a mechanism to tackle errors in the reference labels of the training samples. This was achieved by proposing a novel algorithm to find candidate classification labels of the training samples from their prior probabilities and the currently estimated posteriors on the network and a novel objective function for the optimizations. The algorithm was the result of casting the generalized Kelly criterion for optimal betting into a multiclass classification problem. The proposed objective function was the expected free energy of a prospective active inference and could incorporate the candidate labels, the original reference labels, and the priors of the training samples while still being distribution-based. The incorporation of the priors into the optimization not only helped to tackle errors in the reference labels but also allowed to reduce classification biases towards the dominant classes by focusing the attention of the neural network on important but minority foreground classes.

Visual object tracking has seen significant progress in recent years. However, the vast majority of this work focuses on tracking objects within the image plane of a single camera and ignores the uncertainty associated with predicted object locations. In this work, we focus on the geospatial object tracking problem using data from a distributed camera network. The goal is to predict an object's track in geospatial coordinates along with uncertainty over the object's location while respecting communication constraints that prohibit centralizing raw image data. We present a novel single-object geospatial tracking data set that includes high-accuracy ground truth object locations and video data from a network of four cameras. We present a modeling framework for addressing this task including a novel backbone model and explore how uncertainty calibration and fine-tuning through a differentiable tracker affect performance.

To balance quality and cost, various domain areas of science and engineering run simulations at multiple levels of sophistication. Multi-fidelity active learning aims to learn a direct mapping from input parameters to simulation outputs at the highest fidelity by actively acquiring data from multiple fidelity levels. However, existing approaches based on Gaussian processes are hardly scalable to high-dimensional data. Deep learning-based methods often impose a hierarchical structure in hidden representations, which only supports passing information from low-fidelity to high-fidelity. These approaches can lead to the undesirable propagation of errors from low-fidelity representations to high-fidelity ones. We propose a novel framework called Disentangled Multi-fidelity Deep Bayesian Active Learning (D-MFDAL), which learns the surrogate models conditioned on the distribution of functions at multiple fidelities. On benchmark tasks of learning deep surrogates of partial differential equations including heat equation, Poisson's equation and fluid simulations, our approach significantly outperforms state-of-the-art in prediction accuracy and sample efficiency.

Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty in the parameter values, functional forms with diverse parameterizations, level of complexity needed, and thus in the state fields. We develop a Bayesian model learning methodology that allows interpolation in the space of candidate models and discovery of new models from noisy, sparse, and indirect observations, all while estimating state fields and parameter values, as well as the joint PDFs of all learned quantities. We address the challenges of high-dimensional and multidisciplinary dynamics governed by PDEs by using state augmentation and the computationally efficient GMM-DO filter. Our innovations include stochastic formulation and complexity parameters to unify candidate models into a single general model as well as stochastic expansion parameters within piecewise function approximations to generate dense candidate model spaces. These innovations allow handling many compatible and embedded candidate models, possibly none of which are accurate, and learning elusive unknown functional forms. Our new methodology is generalizable, interpretable, and extrapolates out of the space of models to discover new ones. We perform a series of twin experiments based on flows past a ridge coupled with three-to-five component ecosystem models, including flows with chaotic advection. The probabilities of known, uncertain, and unknown model formulations, and of state fields and parameters, are updated jointly using Bayes' law. Non-Gaussian statistics, ambiguity, and biases are captured. The parameter values and model formulations that best explain the data are identified. When observations are sufficiently informative, model complexity and functions are discovered.

Selecting suitable architecture parameters and training hyperparameters is essential for enhancing machine learning (ML) model performance. Several recent empirical studies conduct large-scale correlational analysis on neural networks (NNs) to search for effective \emph{generalization metrics} that can guide this type of model selection. Effective metrics are typically expected to correlate strongly with test performance. In this paper, we expand on prior analyses by examining generalization-metric-based model selection with the following objectives: (i) focusing on natural language processing (NLP) tasks, as prior work primarily concentrates on computer vision (CV) tasks; (ii) considering metrics that directly predict \emph{test error} instead of the \emph{generalization gap}; (iii) exploring metrics that do not need access to data to compute. From these objectives, we are able to provide the first model selection results on large pretrained Transformers from Huggingface using generalization metrics. Our analyses consider (I) hundreds of Transformers trained in different settings, in which we systematically vary the amount of data, the model size and the optimization hyperparameters, (II) a total of 51 pretrained Transformers from eight families of Huggingface NLP models, including GPT2, BERT, etc., and (III) a total of 28 existing and novel generalization metrics. Despite their niche status, we find that metrics derived from the heavy-tail (HT) perspective are particularly useful in NLP tasks, exhibiting stronger correlations than other, more popular metrics. To further examine these metrics, we extend prior formulations relying on power law (PL) spectral distributions to exponential (EXP) and exponentially-truncated power law (E-TPL) families.

Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable the seamless fusion of different experimental modalities. When the dynamics are discrete and stochastic, one may employ powerful techniques such as Kalman, particle, or variational filters. Practitioners commonly apply these methods to continuous-time, deterministic dynamical systems after discretizing the dynamics and introducing fictitious transition probabilities. However, approaches based on time-discretization suffer from the curse of dimensionality since the number of random variables grows linearly with the number of time-steps. Furthermore, the introduction of fictitious transition probabilities is an unsatisfactory solution because it increases the number of model parameters and may lead to inference bias. To address these drawbacks, the objective of this paper is to develop a scalable Bayesian approach to state and parameter estimation suitable for continuous-time, deterministic dynamical systems. Our methodology builds upon information field theory. Specifically, we construct a physics-informed prior probability measure on the function space of system responses so that functions that satisfy the physics are more likely. This prior allows us to quantify model form errors. We connect the system's response to observations through a probabilistic model of the measurement process. The joint posterior over the system responses and all parameters is given by Bayes' rule. To approximate the intractable posterior, we develop a stochastic variational inference algorithm. In summary, the developed methodology offers a powerful framework for Bayesian estimation in dynamical systems.

Many machine learning problems require performing dataset valuation, i.e. to quantify the incremental gain, to some relevant pre-defined utility, of aggregating an individual dataset to others. As seminal examples, dataset valuation has been leveraged in collaborative and federated learning to create incentives for data sharing across several data owners. The Shapley value has recently been proposed as a principled tool to achieve this goal due to formal axiomatic justification. Since its computation often requires exponential time, standard approximation strategies based on Monte Carlo integration have been considered. Such generic approximation methods, however, remain expensive in some cases. In this paper, we exploit the knowledge about the structure of the dataset valuation problem to devise more efficient Shapley value estimators. We propose a novel approximation of the Shapley value, referred to as discrete uniform Shapley (DU-Shapley) which is expressed as an expectation under a discrete uniform distribution with support of reasonable size. We justify the relevancy of the proposed framework via asymptotic and non-asymptotic theoretical guarantees and show that DU-Shapley tends towards the Shapley value when the number of data owners is large. The benefits of the proposed framework are finally illustrated on several dataset valuation benchmarks. DU-Shapley outperforms other Shapley value approximations, even when the number of data owners is small.