What would have happened if I had acted differently? Although this question is as old as time itself, successful companies have recently embraced this question via counterfactual estimation of outcomes from the exhaust of their controlled experimentation platforms, e.g., based upon A/B testing or contextual bandits. These experiments are run in the real (digital) world, which is rich enough to demand statistical techniques that are non-asymptotic, non-parametric, and non-stationary. Although recent advances admit characterizing counterfactual average outcomes in this general setting, counterfactually estimating a complete distribution of outcomes is heretofore only possible with additional assumptions. Nonethless, the practical importance of this problem has motivated multiple solutions: see Table 1 for a summary, and Section 5 for complete discussion. Intriguingly, this problem is provably impossible in the data dependent setting without additional assumptions. Rakhlin et al. [2015] Consequently, our bounds always achieve non-asymptotic coverage, but may converge to zero width slowly or not at all, depending on the hardness of the instance. We call this design principle AVAST (Always Valid And Sometimes Trivial). In pursuit of our ultimate goal, we derive factual distribution estimators which are useful for estimating the complete distribution of outcomes from direct experience.

Gradients have been exploited in proposal distributions to accelerate the convergence of Markov chain Monte Carlo algorithms on discrete distributions. However, these methods require a natural differentiable extension of the target discrete distribution, which often does not exist or does not provide effective gradient guidance. In this paper, we develop a gradient-like proposal for any discrete distribution without this strong requirement. Built upon a locally-balanced proposal, our method efficiently approximates the discrete likelihood ratio via Newton's series expansion to enable a large and efficient exploration in discrete spaces. We show that our method can also be viewed as a multilinear extension, thus inheriting its desired properties. We prove that our method has a guaranteed convergence rate with or without the Metropolis-Hastings step. Furthermore, our method outperforms a number of popular alternatives in several different experiments, including the facility location problem, extractive text summarization, and image retrieval.

The rising growth of deep neural networks (DNNs) and datasets in size motivates the need for efficient solutions for simultaneous model selection and training. Many methods for hyperparameter optimization (HPO) of iterative learners, including DNNs, attempt to solve this problem by querying and learning a response surface while searching for the optimum of that surface. However, many of these methods make myopic queries, do not consider prior knowledge about the response structure, and/or perform a biased cost-aware search, all of which exacerbate identifying the best-performing model when a total cost budget is specified. This paper proposes a novel approach referred to as {\bf B}udget-{\bf A}ware {\bf P}lanning for {\bf I}terative Learners (BAPI) to solve HPO problems under a constrained cost budget. BAPI is an efficient non-myopic Bayesian optimization solution that accounts for the budget and leverages the prior knowledge about the objective function and cost function to select better configurations and to take more informed decisions during the evaluation (training). Experiments on diverse HPO benchmarks for iterative learners show that BAPI performs better than state-of-the-art baselines in most cases.

Social and real-world considerations such as robustness, fairness, social welfare and multi-agent tradeoffs have given rise to multi-distribution learning paradigms, such as collaborative, group distributionally robust, and fair federated learning. In each of these settings, a learner seeks to minimize its worst-case loss over a set of $n$ predefined distributions, while using as few samples as possible. In this paper, we establish the optimal sample complexity of these learning paradigms and give algorithms that meet this sample complexity. Importantly, our sample complexity bounds exceed that of the sample complexity of learning a single distribution only by an additive factor of $n \log(n) / \epsilon^2$. These improve upon the best known sample complexity of agnostic federated learning by Mohri et al. by a multiplicative factor of $n$, the sample complexity of collaborative learning by Nguyen and Zakynthinou by a multiplicative factor $\log n / \epsilon^3$, and give the first sample complexity bounds for the group DRO objective of Sagawa et al. To achieve optimal sample complexity, our algorithms learn to sample and learn from distributions on demand. Our algorithm design and analysis is enabled by our extensions of stochastic optimization techniques for solving stochastic zero-sum games. In particular, we contribute variants of Stochastic Mirror Descent that can trade off between players' access to cheap one-off samples or more expensive reusable ones.

Reinforcement Learning (RL) agents are often unable to generalise well to environment variations in the state space that were not observed during training. This issue is especially problematic for image-based RL, where a change in just one variable, such as the background colour, can change many pixels in the image. The changed pixels can lead to drastic changes in the agent's latent representation of the image, causing the learned policy to fail. To learn more robust representations, we introduce TEmporal Disentanglement (TED), a self-supervised auxiliary task that leads to disentangled image representations exploiting the sequential nature of RL observations. We find empirically that RL algorithms utilising TED as an auxiliary task adapt more quickly to changes in environment variables with continued training compared to state-of-the-art representation learning methods. Since TED enforces a disentangled structure of the representation, our experiments also show that policies trained with TED generalise better to unseen values of variables irrelevant to the task (e.g. background colour) as well as unseen values of variables that affect the optimal policy (e.g. goal positions).

We derive and solve an ``Equation of Motion'' (EoM) for deep neural networks (DNNs), a differential equation that precisely describes the discrete learning dynamics of DNNs. Differential equations are continuous but have played a prominent role even in the study of discrete optimization (gradient descent (GD) algorithms). However, there still exist gaps between differential equations and the actual learning dynamics of DNNs due to discretization error. In this paper, we start from gradient flow (GF) and derive a counter term that cancels the discretization error between GF and GD. As a result, we obtain EoM, a continuous differential equation that precisely describes the discrete learning dynamics of GD. We also derive discretization error to show to what extent EoM is precise. In addition, we apply EoM to two specific cases: scale- and translation-invariant layers. EoM highlights differences between continuous-time and discrete-time GD, indicating the importance of the counter term for a better description of the discrete learning dynamics of GD. Our experimental results support our theoretical findings.

The graph Transformer emerges as a new architecture and has shown superior performance on various graph mining tasks. In this work, we observe that existing graph Transformers treat nodes as independent tokens and construct a single long sequence composed of all node tokens so as to train the Transformer model, causing it hard to scale to large graphs due to the quadratic complexity on the number of nodes for the self-attention computation. To this end, we propose a Neighborhood Aggregation Graph Transformer (NAGphormer) that treats each node as a sequence containing a series of tokens constructed by our proposed Hop2Token module. For each node, Hop2Token aggregates the neighborhood features from different hops into different representations and thereby produces a sequence of token vectors as one input. In this way, NAGphormer could be trained in a mini-batch manner and thus could scale to large graphs. Moreover, we mathematically show that as compared to a category of advanced Graph Neural Networks (GNNs), the decoupled Graph Convolutional Network, NAGphormer could learn more informative node representations from the multi-hop neighborhoods. Extensive experiments on benchmark datasets from small to large are conducted to demonstrate that NAGphormer consistently outperforms existing graph Transformers and mainstream GNNs. Graphs, as a powerful data structure, are widely used to represent entities and their relations in a variety of domains, such as social networks in sociology and protein-protein interaction networks in biology. Their complex features (e.g., attribute features and topology features) make the graph mining tasks very challenging. Though effective, message passing-based GNNs have a number of inherent limitations, including over-smoothing (Chen et al., 2020a) and over-squashing (Alon & Yahav, 2021) with the increment of model depth, limiting their potential capability for graph representation learning. Though recent efforts (Yang et al., 2020; Lu et al., 2021; Huang et al., 2020; Sun et al., 2022) have been devoted to alleviate the impact of over-smoothing and over-squashing problems, the negative influence of these inherent limitations cannot be eliminated completely.

Federated learning aims to share private data to maximize the data utility without privacy leakage. Previous federated learning research mainly focuses on multi-class classification problems. However, multi-label classification is a crucial research problem close to real-world data properties. Nevertheless, a limited number of federated learning studies explore this research problem. Existing studies of multi-label federated learning did not consider the characteristics of multi-label data, i.e., they used the concept of multi-class classification to verify their methods' performance, which means it will not be feasible to apply their methods to real-world applications. Therefore, this study proposed a new multi-label federated learning framework with a Clustering-based Multi-label Data Allocation (CMDA) and a novel aggregation method, Fast Label-Adaptive Aggregation (FLAG), for multi-label classification in the federated learning environment. The experimental results demonstrate that our methods only need less than 50\% of training epochs and communication rounds to surpass the performance of state-of-the-art federated learning methods.

Regressing the vector field of a dynamical system from a finite number of observed states is a natural way to learn surrogate models for such systems. A simple and interpretable way to learn a dynamical system from data is to interpolate its vector-field with a data-adapted kernel which can be learned by using Kernel Flows. The method of Kernel Flows is a trainable machine learning method that learns the optimal parameters of a kernel based on the premise that a kernel is good if there is no significant loss in accuracy if half of the data is used. The objective function could be a short-term prediction or some other objective for other variants of Kernel Flows). However, this method is limited by the choice of the base kernel. In this paper, we introduce the method of \emph{Sparse Kernel Flows } in order to learn the ``best'' kernel by starting from a large dictionary of kernels. It is based on sparsifying a kernel that is a linear combination of elemental kernels. We apply this approach to a library of 132 chaotic systems.

When humans read a text, their eye movements are influenced by the structural complexity of the input sentences. This cognitive phenomenon holds across languages and recent studies indicate that multilingual language models utilize structural similarities between languages to facilitate cross-lingual transfer. We use sentence-level eye-tracking patterns as a cognitive indicator for structural complexity and show that the multilingual model XLM-RoBERTa can successfully predict varied patterns for 13 typologically diverse languages, despite being fine-tuned only on English data. We quantify the sensitivity of the model to structural complexity and distinguish a range of complexity characteristics. Our results indicate that the model develops a meaningful bias towards sentence length but also integrates cross-lingual differences. We conduct a control experiment with randomized word order and find that the model seems to additionally capture more complex structural information.