Data assimilation (DA) aims at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations taking into account their uncertainties. State of the art methods are based on the Gaussian error statistics and the linearization of the non-linear dynamics which may lead to sub-optimal methods. In this respect, there are still open questions how to improve these methods. In this paper, we propose a fully data driven deep learning architecture generalizing recurrent Elman networks and data assimilation algorithms which approximate a sequence of prior and posterior densities conditioned on noisy observations. By construction our approach can be used for general nonlinear dynamics and non-Gaussian densities. On numerical experiments based on the well-known Lorenz-95 system and with Gaussian error statistics, our architecture achieves comparable performance to EnKF on both the analysis and the propagation of probability density functions of the system state at a given time without using any explicit regularization technique.

Norms, which are culturally accepted guidelines for behaviours, can be integrated into conversational models to generate utterances that are appropriate for the socio-cultural context. Existing methods for norm recognition tend to focus only on surface-level features of dialogues and do not take into account the interactions within a conversation. To address this issue, we propose NormMark, a probabilistic generative Markov model to carry the latent features throughout a dialogue. These features are captured by discrete and continuous latent variables conditioned on the conversation history, and improve the model's ability in norm recognition. The model is trainable on weakly annotated data using the variational technique. On a dataset with limited norm annotations, we show that our approach achieves higher F1 score, outperforming current state-of-the-art methods, including GPT3.

We present a novel perspective and algorithm for learning directed acyclic graphs (DAGs) from data generated by a linear structural equation model (SEM). First, we show that a linear SEM can be viewed as a linear transform that, in prior work, computes the data from a dense input vector of random valued root causes (as we will call them) associated with the nodes. Instead, we consider the case of (approximately) few root causes and also introduce noise in the measurement of the data. Intuitively, this means that the DAG data is produced by few data-generating events whose effect percolates through the DAG. We prove identifiability in this new setting and show that the true DAG is the global minimizer of the $L^0$-norm of the vector of root causes. For data with few root causes, with and without noise, we show superior performance compared to prior DAG learning methods.

Training visual reinforcement learning (RL) models in offline datasets is challenging due to overfitting issues in representation learning and overestimation problems in value function. In this paper, we propose a transfer learning method called Collaborative World Models (CoWorld) to improve the performance of visual RL under offline conditions. The core idea is to use an easy-to-interact, off-the-shelf simulator to train an auxiliary RL model as the online "test bed" for the offline policy learned in the target domain, which provides a flexible constraint for the value function -- Intuitively, we want to mitigate the overestimation problem of value functions outside the offline data distribution without impeding the exploration of actions with potential advantages. Specifically, CoWorld performs domain-collaborative representation learning to bridge the gap between online and offline hidden state distributions. Furthermore, it performs domain-collaborative behavior learning that enables the source RL agent to provide target-aware value estimation, allowing for effective offline policy regularization. Experiments show that CoWorld significantly outperforms existing methods in offline visual control tasks in DeepMind Control and Meta-World.

Most reinforcement learning algorithms treat the context under which they operate as a stationary, isolated and undisturbed environment. However, in the real world, the environment is constantly changing due to a variety of external influences. To address this problem, we study Markov Decision Processes (MDP) under the influence of an external temporal process. We formalize this notion and discuss conditions under which the problem becomes tractable with suitable solutions. We propose a policy iteration algorithm to solve this problem and theoretically analyze its performance.

It is typically understood that the training of modern neural networks is a process of fitting the probability distribution of desired output. However, recent paradoxical observations in a number of language generation tasks let one wonder if this canonical probability-based explanation can really account for the empirical success of deep learning. To resolve this issue, we propose an alternative utility-based explanation to the standard supervised learning procedure in deep learning. The basic idea is to interpret the learned neural network not as a probability model but as an ordinal utility function that encodes the preference revealed in training data. In this perspective, training of the neural network corresponds to a utility learning process. Specifically, we show that for all neural networks with softmax outputs, the SGD learning dynamic of maximum likelihood estimation (MLE) can be seen as an iteration process that optimizes the neural network toward an optimal utility function. This utility-based interpretation can explain several otherwise-paradoxical observations about the neural networks thus trained. Moreover, our utility-based theory also entails an equation that can transform the learned utility values back to a new kind of probability estimation with which probability-compatible decision rules enjoy dramatic (double-digits) performance improvements. These evidences collectively reveal a phenomenon of utility-probability duality in terms of what modern neural networks are (truly) modeling: We thought they are one thing (probabilities), until the unexplainable showed up; changing mindset and treating them as another thing (utility values) largely reconcile the theory, despite remaining subtleties regarding its original (probabilistic) identity.

The task of drawing samples efficiently from high-dimensional complex probability distributions enables us to perform inference using complex statistical models from large amounts of data, where uncertainty quantification is of paramount importance to understand the intrinsic risk associated with every decision made with models learned from data. The ability to quantify uncertainty when comparing a theoretical or computational model to observations is critical to conducting a sound scientific investigation, particularly in machine-learned models and in the physical sciences like physics [92]. More specifically, Bayesian inference [96, 184] is a prominent method for linking models and observations and estimating uncertainties, in which sampling techniques are widely adopted, which also finds applications to various areas such as imaging processing and inverse problems (see e.g., [87]), and Bayesian neural networks and deep learning [134], etc. While Markov chain Monte Carlo (MCMC) methods [164] have been the major workhorse of such sampling tasks, most traditional MCMC algorithms were regarded as unscalable to high dimensions. In particular, in modern large-scale applications such as Bayesian deep learning in the overparameterized regime in which we want to make posterior inference on the neural network weights, traditional MCMC algorithms become computationally prohibitive in such high dimensions and alternative approaches such as variational inference (VI; see e.g., [21]) have been widely adopted.

In this paper, we investigate a scenario in which a robot learns a low-dimensional representation of a door given a video of the door opening or closing. This representation can be used to infer door-related parameters and predict the outcomes of interacting with the door. Current machine learning based approaches in the doors domain are based primarily on labelled datasets. However, the large quantity of available door data suggests the feasibility of a semisupervised approach based on pretraining. To exploit the hierarchical structure of the dataset where each door has multiple associated images, we pretrain with a structured latent variable model known as a neural statistician. The neural satsitician enforces separation between shared context-level variables (common across all images associated with the same door) and instance-level variables (unique to each individual image). We first demonstrate that the neural statistician is able to learn an embedding that enables reconstruction and sampling of realistic door images. Then, we evaluate the correspondence of the learned embeddings to human-interpretable parameters in a series of supervised inference tasks. It was found that a pretrained neural statistician encoder outperformed analogous context-free baselines when predicting door handedness, size, angle location, and configuration from door images. Finally, in a visual bandit door-opening task with a variety of door configuration, we found that neural statistician embeddings achieve lower regret than context-free baselines.

Machine-learned systems are in widespread use for making decisions about humans, and it is important that they are fair, i.e., not biased against individuals based on sensitive attributes. We present runtime verification of algorithmic fairness for systems whose models are unknown, but are assumed to have a Markov chain structure. We introduce a specification language that can model many common algorithmic fairness properties, such as demographic parity, equal opportunity, and social burden. We build monitors that observe a long sequence of events as generated by a given system, and output, after each observation, a quantitative estimate of how fair or biased the system was on that run until that point in time. The estimate is proven to be correct modulo a variable error bound and a given confidence level, where the error bound gets tighter as the observed sequence gets longer. Our monitors are of two types, and use, respectively, frequentist and Bayesian statistical inference techniques. While the frequentist monitors compute estimates that are objectively correct with respect to the ground truth, the Bayesian monitors compute estimates that are correct subject to a given prior belief about the system's model. Using a prototype implementation, we show how we can monitor if a bank is fair in giving loans to applicants from different social backgrounds, and if a college is fair in admitting students while maintaining a reasonable financial burden on the society. Although they exhibit different theoretical complexities in certain cases, in our experiments, both frequentist and Bayesian monitors took less than a millisecond to update their verdicts after each observation.

Cooperative multi-agent reinforcement learning (MARL) is a challenging task, as agents must learn complex and diverse individual strategies from a shared team reward. However, existing methods struggle to distinguish and exploit important individual experiences, as they lack an effective way to decompose the team reward into individual rewards. To address this challenge, we propose DIFFER, a powerful theoretical framework for decomposing individual rewards to enable fair experience replay in MARL. By enforcing the invariance of network gradients, we establish a partial differential equation whose solution yields the underlying individual reward function. The individual TD-error can then be computed from the solved closed-form individual rewards, indicating the importance of each piece of experience in the learning task and guiding the training process. Our method elegantly achieves an equivalence to the original learning framework when individual experiences are homogeneous, while also adapting to achieve more muscular efficiency and fairness when diversity is observed.Our extensive experiments on popular benchmarks validate the effectiveness of our theory and method, demonstrating significant improvements in learning efficiency and fairness.