Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters, initial and boundary conditions that cannot be simply averaged out. We introduce a randomised adaptive group Lasso sparsity estimator to promote grouped sparsity and implement it in a deep learning based PDE discovery framework. It allows to create a learning bias that implies the a priori assumption that all experiments can be explained by the same underlying PDE terms with potentially different coefficients. Our experimental results show more generalizable PDEs can be found from multiple highly noisy datasets, by this grouped sparsity promotion rather than simply performing independent model discoveries.
Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and processes that data using a quantum computer, could have significant advantages over conventional experiments in which the physical system is measured and the outcomes are processed using a classical computer. We prove that, in various tasks, quantum machines can learn from exponentially fewer experiments than those required in conventional experiments. The exponential advantage holds in predicting properties of physical systems, performing quantum principal component analysis on noisy states, and learning approximate models of physical dynamics. In some tasks, the quantum processing needed to achieve the exponential advantage can be modest; for example, one can simultaneously learn about many noncommuting observables by processing only two copies of the system. Conducting experiments with up to 40 superconducting qubits and 1300 quantum gates, we demonstrate that a substantial quantum advantage can be realized using today's relatively noisy quantum processors. Our results highlight how quantum technology can enable powerful new strategies to learn about nature.
A fundamental problem in statistics is to compare the outcomes attained by members of subpopulations. This problem arises in the analysis of randomized controlled trials, in the analysis of A/B tests, and in the assessment of fairness and bias in the treatment of sensitive subpopulations, especially when measuring the effects of algorithms and machine learning. Often the comparison makes the most sense when performed separately for individuals who are similar according to certain characteristics given by the values of covariates of interest; the separate comparisons can also be aggregated in various ways to compare across all values of the covariates. Separating, segmenting, or stratifying into those with similar values of the covariates is also known as "conditioning on" or "controlling for" those covariates; controlling for age or annual income is common. Two standard methods of controlling for covariates are (1) binning and (2) regression modeling. Binning requires making fairly arbitrary, yet frequently highly influential choices, and is unsatisfactorily temperamental in multiple dimensions, with multiple covariates. Regression analysis works wonderfully when there is good reason to believe in a particular parameterized regression model or classifier (such as logistic regression). Thus, there appears to be no extant canonical fully non-parametric regression for the comparison of subpopulations, not while conditioning on multiple specified covariates. Existing methods rely on analysts to make choices, and those choices can be debatable; analysts can deceive others or even themselves. The present paper aims to fill the gap, combining two ingredients: (1) recently developed methodologies for such comparisons that already exist when conditioning on a single scalar covariate and (2) the Hilbert space-filling curve that maps continuously from one dimension to multiple dimensions.
Learning the structure of a Bayesian Network (BN) with score-based solutions involves exploring the search space of possible graphs and moving towards the graph that maximises a given objective function. Some algorithms offer exact solutions that guarantee to return the graph with the highest objective score, while others offer approximate solutions in exchange for reduced computational complexity. This paper describes an approximate BN structure learning algorithm, which we call Model Averaging Hill-Climbing (MAHC), that combines two novel strategies with hill-climbing search. The algorithm starts by pruning the search space of graphs, where the pruning strategy can be viewed as an aggressive version of the pruning strategies that are typically applied to combinatorial optimisation structure learning problems. It then performs model averaging in the hill-climbing search process and moves to the neighbouring graph that maximises the objective function, on average, for that neighbouring graph and over all its valid neighbouring graphs. Comparisons with other algorithms spanning different classes of learning suggest that the combination of aggressive pruning with model averaging is both effective and efficient, particularly in the presence of data noise.
Unsupervised learning is often used to uncover clusters in data. However, different kinds of noise may impede the discovery of useful patterns from real-world time-series data. In this work, we focus on mitigating the interference of interval censoring in the task of clustering for disease phenotyping. We develop a deep generative, continuous-time model of time-series data that clusters time-series while correcting for censorship time. We provide conditions under which clusters and the amount of delayed entry may be identified from data under a noiseless model.
Humans show an innate ability to learn the regularities of the world through interaction. By performing experiments in our environment, we are able to discern the causal factors of variation and infer how they affect the dynamics of our world. Analogously, here we attempt to equip reinforcement learning agents with the ability to perform experiments that facilitate a categorization of the rolled-out trajectories, and to subsequently infer the causal factors of the environment in a hierarchical manner. We introduce a novel intrinsic reward, called causal curiosity, and show that it allows our agents to learn optimal sequences of actions, and to discover causal factors in the dynamics. The learned behavior allows the agent to infer a binary quantized representation for the ground-truth causal factors in every environment. Additionally, we find that these experimental behaviors are semantically meaningful (e.g., to differentiate between heavy and light blocks, our agents learn to lift them), and are learnt in a self-supervised manner with approximately 2.5 times less data than conventional supervised planners. We show that these behaviors can be re-purposed and fine-tuned (e.g., from lifting to pushing or other downstream tasks). Finally, we show that the knowledge of causal factor representations aids zero-shot learning for more complex tasks.
Convolutional Neural Networks experience catastrophic forgetting when optimized on a sequence of learning problems: as they meet the objective of the current training examples, their performance on previous tasks drops drastically. In this work, we introduce a novel framework to tackle this problem with conditional computation. We equip each convolutional layer with task-specific gating modules, selecting which filters to apply on the given input. This way, we achieve two appealing properties. Firstly, the execution patterns of the gates allow to identify and protect important filters, ensuring no loss in the performance of the model for previously learned tasks. Secondly, by using a sparsity objective, we can promote the selection of a limited set of kernels, allowing to retain sufficient model capacity to digest new tasks.Existing solutions require, at test time, awareness of the task to which each example belongs to. This knowledge, however, may not be available in many practical scenarios. Therefore, we additionally introduce a task classifier that predicts the task label of each example, to deal with settings in which a task oracle is not available. We validate our proposal on four continual learning datasets. Results show that our model consistently outperforms existing methods both in the presence and the absence of a task oracle. Notably, on Split SVHN and Imagenet-50 datasets, our model yields up to 23.98% and 17.42% improvement in accuracy w.r.t. competing methods.
Discovering causal structure among a set of variables is a fundamental problem in many empirical sciences. Traditional score-based casual discovery methods rely on various local heuristics to search for a Directed Acyclic Graph (DAG) according to a predefined score function. While these methods, e.g., greedy equivalence search, may have attractive results with infinite samples and certain model assumptions, they are usually less satisfactory in practice due to finite data and possible violation of assumptions. Motivated by recent advances in neural combinatorial optimization, we propose to use Reinforcement Learning (RL) to search for the DAG with the best scoring. Our encoder-decoder model takes observable data as input and generates graph adjacency matrices that are used to compute rewards. The reward incorporates both the predefined score function and two penalty terms for enforcing acyclicity. In contrast with typical RL applications where the goal is to learn a policy, we use RL as a search strategy and our final output would be the graph, among all graphs generated during training, that achieves the best reward. We conduct experiments on both synthetic and real datasets, and show that the proposed approach not only has an improved search ability but also allows a flexible score function under the acyclicity constraint.
Data association-based multiple object tracking (MOT) involves multiple separated modules processed or optimized differently, which results in complex method design and requires non-trivial tuning of parameters. In this paper, we present an end-to-end model, named FAMNet, where Feature extraction, Affinity estimation and Multi-dimensional assignment are refined in a single network. All layers in FAMNet are designed differentiable thus can be optimized jointly to learn the discriminative features and higher-order affinity model for robust MOT, which is supervised by the loss directly from the assignment ground truth. We also integrate single object tracking technique and a dedicated target management scheme into the FAMNet-based tracking system to further recover false negatives and inhibit noisy target candidates generated by the external detector. The proposed method is evaluated on a diverse set of benchmarks including MOT2015, MOT2017, KITTI-Car and UA-DETRAC, and achieves promising performance on all of them in comparison with state-of-the-arts.
To solve complex real-world problems with reinforcement learning, we cannot rely on manually specified reward functions. Instead, we can have humans communicate an objective to the agent directly. In this work, we combine two approaches to learning from human feedback: expert demonstrations and trajectory preferences. We train a deep neural network to model the reward function and use its predicted reward to train an DQN-based deep reinforcement learning agent on 9 Atari games. Our approach beats the imitation learning baseline in 7 games and achieves strictly superhuman performance on 2 games without using game rewards. Additionally, we investigate the goodness of fit of the reward model, present some reward hacking problems, and study the effects of noise in the human labels.
Recent studies have shown the vulnerability of reinforcement learning (RL) models in noisy settings. The sources of noises differ across scenarios. For instance, in practice, the observed reward channel is often subject to noise (e.g., when observed rewards are collected through sensors), and thus observed rewards may not be credible as a result. Also, in applications such as robotics, a deep reinforcement learning (DRL) algorithm can be manipulated to produce arbitrary errors. In this paper, we consider noisy RL problems where observed rewards by RL agents are generated with a reward confusion matrix. We call such observed rewards as perturbed rewards. We develop an unbiased reward estimator aided robust RL framework that enables RL agents to learn in noisy environments while observing only perturbed rewards. Our framework draws upon approaches for supervised learning with noisy data. The core ideas of our solution include estimating a reward confusion matrix and defining a set of unbiased surrogate rewards. We prove the convergence and sample complexity of our approach. Extensive experiments on different DRL platforms show that policies based on our estimated surrogate reward can achieve higher expected rewards, and converge faster than existing baselines. For instance, the state-of-the-art PPO algorithm is able to obtain 67.5% and 46.7% improvements in average on five Atari games, when the error rates are 10% and 30% respectively.