A mainstream type of current self-supervised learning methods pursues a general-purpose representation that can be well transferred to downstream tasks, typically by optimizing on a given pretext task such as instance discrimination. In this work, we argue that existing pretext tasks inevitably introduce biases into the learned representation, which in turn leads to biased transfer performance on various downstream tasks. To cope with this issue, we propose Maximum Entropy Coding (MEC), a more principled objective that explicitly optimizes on the structure of the representation, so that the learned representation is less biased and thus generalizes better to unseen downstream tasks. Inspired by the principle of maximum entropy in information theory, we hypothesize that a generalizable representation should be the one that admits the maximum entropy among all plausible representations. To make the objective end-to-end trainable, we propose to leverage the minimal coding length in lossy data coding as a computationally tractable surrogate for the entropy, and further derive a scalable reformulation of the objective that allows fast computation. Extensive experiments demonstrate that MEC learns a more generalizable representation than previous methods based on specific pretext tasks. It achieves state-of-the-art performance consistently on various downstream tasks, including not only ImageNet linear probe, but also semi-supervised classification, object detection, instance segmentation, and object tracking. Interestingly, we show that existing batch-wise and feature-wise self-supervised objectives could be seen equivalent to low-order approximations of MEC. Code and pre-trained models are available at https://github.com/xinliu20/MEC.

Heterogeneous graph neural networks (GNNs) achieve strong performance on node classification tasks in a semi-supervised learning setting. However, as in the simpler homogeneous GNN case, message-passing-based heterogeneous GNNs may struggle to balance between resisting the oversmoothing that may occur in deep models, and capturing long-range dependencies of graph structured data. Moreover, the complexity of this trade-off is compounded in the heterogeneous graph case due to the disparate heterophily relationships between nodes of different types. To address these issues, we propose a novel heterogeneous GNN architecture in which layers are derived from optimization steps that descend a novel relation-aware energy function. The corresponding minimizer is fully differentiable with respect to the energy function parameters, such that bilevel optimization can be applied to effectively learn a functional form whose minimum provides optimal node representations for subsequent classification tasks. In particular, this methodology allows us to model diverse heterophily relationships between different node types while avoiding oversmoothing effects. Experimental results on 8 heterogeneous graph benchmarks demonstrates that our proposed method can achieve competitive node classification accuracy

We study the generalisation properties of majority voting on finite ensembles of classifiers, proving margin-based generalisation bounds via the PAC-Bayes theory. These provide state-of-the-art guarantees on a number of classification tasks. Our central results leverage the Dirichlet posteriors studied recently by Zantedeschi et al. [2021] for training voting classifiers; in contrast to that work our bounds apply to non-randomised votes via the use of margins. Our contributions add perspective to the debate on the "margins theory" proposed by Schapire et al. [1998] for the generalisation of ensemble classifiers.

Causal discovery aims to recover causal structures generating the observational data. Despite its success in certain problems, in many real-world scenarios the observed variables are not the target variables of interest, but the imperfect measures of the target variables. Causal discovery under measurement error aims to recover the causal graph among unobserved target variables from observations made with measurement error. We consider a specific formulation of the problem, where the unobserved target variables follow a linear non-Gaussian acyclic model, and the measurement process follows the random measurement error model. Existing methods on this formulation rely on non-scalable over-complete independent component analysis (OICA). In this work, we propose the Transformed Independent Noise (TIN) condition, which checks for independence between a specific linear transformation of some measured variables and certain other measured variables. By leveraging the non-Gaussianity and higher-order statistics of data, TIN is informative about the graph structure among the unobserved target variables. By utilizing TIN, the ordered group decomposition of the causal model is identifiable. In other words, we could achieve what once required OICA to achieve by only conducting independence tests. Experimental results on both synthetic and real-world data demonstrate the effectiveness and reliability of our method.

Submodular functions and variants, through their ability to characterize diversity and coverage, have emerged as a key tool for data selection and summarization. Many recent approaches to learn submodular functions suffer from limited expressiveness. In this work, we propose FLEXSUBNET, a family of flexible neural models for both monotone and non-monotone submodular functions. To fit a latent submodular function from (set, value) observations, FLEXSUBNET applies a concave function on modular functions in a recursive manner. We do not draw the concave function from a restricted family, but rather learn from data using a highly expressive neural network that implements a differentiable quadrature procedure. Such an expressive neural model for concave functions may be of independent interest. Next, we extend this setup to provide a novel characterization of monotone \alpha-submodular functions, a recently introduced notion of approximate submodular functions. We then use this characterization to design a novel neural model for such functions. Finally, we consider learning submodular set functions under distant supervision in the form of (perimeter-set, high-value-subset) pairs. This yields a novel subset selection method based on an order-invariant, yet greedy sampler built around the above neural set functions. Our experiments on synthetic and real data show that FLEXSUBNET outperforms several baselines.

In this paper, we address the dichotomy between heterogeneous models and simultaneous training in Federated Learning (FL) via a clustering framework. We define a new clustering model for FL based on the (optimal) local models of the users: two users belong to the same cluster if their local models are close; otherwise they belong to different clusters. A standard algorithm for clustered FL is proposed in \cite{ghosh_efficient_2021}, called \texttt{IFCA}, which requires \emph{suitable} initialization and the knowledge of hyper-parameters like the number of clusters (which is often quite difficult to obtain in practical applications) to converge. We propose an improved algorithm, \emph{Successive Refine Federated Clustering Algorithm} (\texttt{SR-FCA}), which removes such restrictive assumptions. \texttt{SR-FCA} treats each user as a singleton cluster as an initialization, and then successively refine the cluster estimation via exploiting similar users belonging to the same cluster. In any intermediate step, \texttt{SR-FCA} uses a robust federated learning algorithm within each cluster to exploit simultaneous training and to correct clustering errors. Furthermore, \texttt{SR-FCA} does not require any \emph{good} initialization (warm start), both in theory and practice. We show that with proper choice of learning rate, \texttt{SR-FCA} incurs arbitrarily small clustering error. Additionally, we validate the performance of our algorithm on standard FL datasets in non-convex problems like neural nets, and we show the benefits of \texttt{SR-FCA} over baselines.

In the machine learning literature stochastic gradient descent has recently been widely discussed for its purported implicit regularization properties. Much of the theory, that attempts to clarify the role of noise in stochastic gradient algorithms, has widely approximated stochastic gradient descent by a stochastic differential equation with Gaussian noise. We provide a novel rigorous theoretical justification for this practice that showcases how the Gaussianity of the noise arises naturally.

We consider distributed learning using constant stepsize SGD (DSGD) over several devices, each sending a final model update to a central server. In a final step, the local estimates are aggregated. We prove in the setting of overparameterized linear regression general upper bounds with matching lower bounds and derive learning rates for specific data generating distributions. We show that the excess risk is of order of the variance provided the number of local nodes grows not too large with the global sample size. We further compare the sample complexity of DSGD with the sample complexity of distributed ridge regression (DRR) and show that the excess SGD-risk is smaller than the excess RR-risk, where both sample complexities are of the same order.

In the past few years, graph neural networks (GNNs) have become the de facto model of choice for graph classification. While, from the theoretical viewpoint, most GNNs can operate on graphs of any size, it is empirically observed that their classification performance degrades when they are applied on graphs with sizes that differ from those in the training data. Previous works have tried to tackle this issue in graph classification by providing the model with inductive biases derived from assumptions on the generative process of the graphs, or by requiring access to graphs from the test domain. The first strategy is tied to the quality of the assumptions made for the generative process, and requires the use of specific models designed after the explicit definition of the generative process of the data, leaving open the question of how to improve the performance of generic GNN models in general settings. On the other hand, the second strategy can be applied to any GNN, but requires access to information that is not always easy to obtain. In this work we consider the scenario in which we only have access to the training data, and we propose a regularization strategy that can be applied to any GNN to improve its generalization capabilities from smaller to larger graphs without requiring access to the test data. Our regularization is based on the idea of simulating a shift in the size of the training graphs using coarsening techniques, and enforcing the model to be robust to such a shift. Experimental results on standard datasets show that popular GNN models, trained on the 50% smallest graphs in the dataset and tested on the 10% largest graphs, obtain performance improvements of up to 30% when trained with our regularization strategy.

As machine learning becomes more widely adopted across domains, it is critical that researchers and ML engineers think about the inherent biases in the data that may be perpetuated by the model. Recently, many studies have shown that such biases are also imbibed in Graph Neural Network (GNN) models if the input graph is biased, potentially to the disadvantage of underserved and underrepresented communities. In this work, we aim to mitigate the bias learned by GNNs by jointly optimizing two different loss functions: one for the task of link prediction and one for the task of demographic parity. We further implement three different techniques inspired by graph modification approaches: the Global Fairness Optimization (GFO), Constrained Fairness Optimization (CFO), and Fair Edge Weighting (FEW) models. These techniques mimic the effects of changing underlying graph structures within the GNN and offer a greater degree of interpretability over more integrated neural network methods. Our proposed models emulate microscopic or macroscopic edits to the input graph while training GNNs and learn node embeddings that are both accurate and fair under the context of link recommendations. We demonstrate the effectiveness of our approach on four real world datasets and show that we can improve the recommendation fairness by several factors at negligible cost to link prediction accuracy.