ICML 2023 Papers

We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is to cluster a set of objects based on multiway interactions of different categories or types. We present improved approximation guarantees based on linear programming, and show they are tight by proving a matching integrality gap. Our results also include new approximation hardness results, a combinatorial 2-approximation whose runtime is linear in the hypergraph size, and several new connections to well-studied objectives such as vertex cover and hypergraph multiway cut.

Given a pre-trained in-distribution (ID) model, the inference-time out-of-distribution (OOD) detection aims to recognize OOD data during the inference stage. However, some representative methods share an unproven assumption that the probability that OOD data belong to every ID class should be the same, i.e., these OOD-to-ID probabilities actually form a uniform distribution. In this paper, we show that this assumption makes the above methods incapable when the ID model is trained with class-imbalanced data.Fortunately, by analyzing the causal relations between ID/OOD classes and features, we identify several common scenarios where the OOD-to-ID probabilities should be the ID-class-prior distribution and propose two strategies to modify existing inference-time detection methods: 1) replace the uniform distribution with the ID-class-prior distribution if they explicitly use the uniform distribution; 2) otherwise, reweight their scores according to the similarity between the ID-class-prior distribution and the softmax outputs of the pre-trained model. Extensive experiments show that both strategies can improve the OOD detection performance when the ID model is pre-trained with imbalanced data, reflecting the importance of ID-class prior in OOD detection.

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. Detecting such singularities is therefore crucial as a precursor to interpolation and inference tasks. We address this issue by developing a topological framework that (i) quantifies the local intrinsic dimension, and (ii) yields a Euclidicity score for assessing the 'manifoldness' of a point along multiple scales. Our approach identifies singularities of complex spaces, while also capturing singular structures and local geometric complexity in image data.

We study the problem of privately estimating the parameters of $d$-dimensional Gaussian Mixture Models (GMMs) with $k$ components. For this, we develop a technique to reduce the problem to its non-private counterpart. This allows us to privatize existing non-private algorithms in a blackbox manner, while incurring only a small overhead in the sample complexity and running time. As the main application of our framework, we develop an $(\varepsilon, \delta)$-differentially private algorithm to learn GMMs using the non-private algorithm of Moitra and Valiant (2010) as a blackbox. Consequently, this gives the first sample complexity upper bound and first polynomial time algorithm for privately learning GMMs without any boundedness assumptions on the parameters. As part of our analysis, we prove a tight (up to a constant factor) lower bound on the total variation distance of high-dimensional Gaussians which can be of independent interest.

We present a simple picture of the training process of self-supervised learning methods with dual deep networks. In our picture, these methods learn their high-dimensional embeddings one dimension at a time in a sequence of discrete, well-separated steps. We arrive at this picture via the study of a linear toy model of Barlow Twins, applicable to the case in which the trained network is infinitely wide. We solve the training dynamics of our toy model from small initialization, finding that the model learns the top eigenmodes of a certain contrastive kernel in a discrete, stepwise fashion, and find a closed-form expression for the final learned representations. Remarkably, we see the same stepwise learning phenomenon when training deep ResNets using the Barlow Twins, SimCLR, and VICReg losses. This stepwise picture partially demystifies the process of self-supervised training.

Unlearning algorithms aim to remove deleted data's influence from trained models at a cost lower than full retraining. However, prior guarantees of unlearning in literature are flawed and don't protect the privacy of deleted records. We show that when people delete their data as a function of published models, records in a database become interdependent. So, even retraining a fresh model after deletion of a record doesn't ensure its privacy. Secondly, unlearning algorithms that cache partial computations to speed up the processing can leak deleted information over a series of releases, violating the privacy of deleted records in the long run. To address these, we propose a sound deletion guarantee and show that ensuring the privacy of existing records is necessary for the privacy of deleted records. Under this notion, we propose an optimal, computationally efficient, and sound machine unlearning algorithm based on noisy gradient descent.

Modeling spatiotemporal dynamics with neural differential equations has become a major line of research that opens new ways to handle various real-world scenarios (e.g., missing observations, irregular times, etc.). Despite such progress, most existing methods still face challenges in providing a general framework for analyzing time series. To tackle this, we adopt stochastic differential games to suggest a new philosophy of utilizing interacting collective intelligence in time series analysis. For the implementation, we develop the novel gradient descent-based algorithm called deep neural fictitious play to approximate the Nash equilibrium. We theoretically analyze the convergence result of the proposed algorithm and discuss the advantage of cooperative games in handling noninformative observation. Throughout the experiments on various datasets, we demonstrate the superiority of our framework over all the tested benchmarks in modeling time-series prediction by capitalizing on the advantages of applying cooperative games. An ablation study shows that neural agents of the proposed framework learn intrinsic temporal relevance to make accurate time-series predictions.

Ensembling is among the most popular tools in machine learning (ML) due to its effectiveness in minimizing variance and thus improving generalization. Most ensembling methods for black-box base learners fall under the umbrella of "stacked generalization," namely training an ML algorithm that takes the inferences from the base learners as input. While stacking has been widely applied in practice, its theoretical properties are poorly understood. In this paper, we prove a novel result, showing that choosing the best stacked generalization from a (finite or finite-dimensional) family of stacked generalizations based on cross-validated performance does not perform "much worse" than the oracle best. Our result strengthens and significantly extends the results in Van der Laan et al. (2007). Inspired by the theoretical analysis, we further propose a particular family of stacked generalizations in the context of probabilistic forecasting, each one with a different sensitivity for how much the ensemble weights are allowed to vary across items, timestamps in the forecast horizon, and quantiles. Experimental results demonstrate the performance gain of the proposed method.

Unsupervised domain adaptation (UDA) enables the transfer of models trained on source domains to unlabeled target domains. However, transferring complex time series models presents challenges due to the dynamic temporal structure variations across domains. This leads to feature shifts in the time and frequency representations. Additionally, the label distributions of tasks in the source and target domains can differ significantly, posing difficulties in addressing label shifts and recognizing labels unique to the target domain. Effectively transferring complex time series models remains a formidable problem. We present RAINCOAT, the first model for both closed-set and universal domain adaptation on complex time series. RAINCOAT addresses feature and label shifts by considering both temporal and frequency features, aligning them across domains, and correcting for misalignments to facilitate the detection of private labels. Additionally, RAINCOAT improves transferability by identifying label shifts in target domains. Our experiments with 5 datasets and 13 state-of-the-art UDA methods demonstrate that RAINCOAT can improve transfer learning performance by up to 16.33% and can handle both closed-set and universal domain adaptation.

The Johnson-Lindenstaruss lemma (Johnson & Lindenstrauss, 1984) is a cornerstone result in dimensionality reduction, stating it is possible to embed a set of $n$ points in $d$-dimensional Euclidean space into optimal $k=O(\varepsilon^{-2} \ln n)$ dimensions, while preserving all pairwise distances to within a factor $(1 \pm \varepsilon)$. The seminal Fast Johnson-Lindenstrauss (Fast JL) transform by Ailon and Chazelle (SICOMP'09) supports computing the embedding of a data point in $O(d \ln d +k \ln^2 n)$ time, where the $d \ln d$ term comes from multiplication with a $d \times d$ Hadamard matrix and the $k \ln^2 n$ term comes from multiplication with a sparse $k \times d$ matrix. Despite the Fast JL transform being more than a decade old, it is one of the fastest dimensionality reduction techniques for many tradeoffs between $\varepsilon, d$ and $n$. In this work, we give a surprising new analysis of the Fast JL transform, showing that the $k \ln^2 n$ term in the embedding time can be improved to $(k \ln^2 n)/\alpha$ for an $\alpha = \Omega(\min\{\varepsilon^{-1}\ln(1/\varepsilon), \ln n\})$. The improvement follows by using an even sparser matrix. We complement our improved analysis with a lower bound showing that our new analysis is in fact tight.

Explaining predictions based on multivariate time series data carries the additional difficulty of handling not only multiple features, but also time dependencies. It matters not only what happened, but also when, and the same feature could have a very different impact on a prediction depending on this time information. Previous work has used perturbation-based saliency methods to tackle this issue, perturbing an input using a trainable mask to discover which features at which times are driving the predictions. However these methods introduce fixed perturbations, inspired from similar methods on static data, while there seems to be little motivation to do so on temporal data. In this work, we aim to explain predictions by learning not only masks, but also associated perturbations. We empirically show that learning these perturbations significantly improves the quality of these explanations on time series data.

Self-supervised learning (SSL) for clinical time series data has received significant attention in recent literature, since these data are highly rich and provide important information about a patient's physiological state. However, most existing SSL methods for clinical time series are limited in that they are designed for unimodal time series, such as a sequence of structured features (e.g., lab values and vitals signs) or an individual high-dimensional physiological signal (e.g., an electrocardiogram). These existing methods cannot be readily extended to model time series that exhibit multimodality, with structured features and high-dimensional data being recorded at each timestep in the sequence. In this work, we address this gap and propose a new SSL method --- Sequential Multi-Dimensional SSL --- where a SSL loss is applied both at the level of the entire sequence and at the level of the individual high-dimensional data points in the sequence in order to better capture information at both scales. Our strategy is agnostic to the specific form of loss function used at each level -- it can be contrastive, as in SimCLR, or non-contrastive, as in VICReg. We evaluate our method on two real-world clinical datasets, where the time series contains sequences of (1) high-frequency electrocardiograms and (2) structured data from lab values and vitals signs. Our experimental results indicate that pre-training with our method and then fine-tuning on downstream tasks improves performance over baselines on both datasets, and in several settings, can lead to improvements across different self-supervised loss functions.

Selecting informative data points for expert feedback can significantly improve the performance of anomaly detection (AD) in various contexts, such as medical diagnostics or fraud detection. In this paper, we determine a set of theoretical conditions under which anomaly scores generalize from labeled queries to unlabeled data. Motivated by these results, we propose a data labeling strategy with optimal data coverage under labeling budget constraints. In addition, we propose a new learning framework for semi-supervised AD. Extensive experiments on image, tabular, and video data sets show that our approach results in state-of-the-art semi-supervised AD performance under labeling budget constraints.

We consider test-time adaptation (TTA), the task of adapting a trained model to an arbitrary test domain using unlabeled input data on-the-fly during testing. A common practice of TTA is to disregard data used in training due to large memory demand and privacy leakage. However, the training data are the only source of supervision. This motivates us to investigate a proper way of using them while minimizing the side effects. To this end, we propose two lightweight yet informative proxies of the training data and a TTA method fully exploiting them. One of the proxies is composed of a small number of images synthesized (hence, less privacy-sensitive) by data condensation which minimizes their domain-specificity to capture a general underlying structure over a wide spectrum of domains. Then, in TTA, they are translated into labeled test data by stylizing them to match styles of unlabeled test samples. This enables virtually supervised test-time training. The other proxy is inter-class relations of training data, which are transferred to target model during TTA. On four public benchmarks, our method outperforms the state-of-the-art ones at remarkably less computation and memory.

Due to the unsupervised nature of anomaly detection, the key to fueling deep models is finding supervisory signals. Different from current reconstruction-guided generative models and transformation-based contrastive models, we devise novel data-driven supervision for tabular data by introducing a characteristic -- scale -- as data labels. By representing varied sub-vectors of data instances, we define scale as the relationship between the dimensionality of original sub-vectors and that of representations. Scales serve as labels attached to transformed representations, thus offering ample labeled data for neural network training. This paper further proposes a scale learning-based anomaly detection method. Supervised by the learning objective of scale distribution alignment, our approach learns the ranking of representations converted from varied subspaces of each data instance. Through this proxy task, our approach models inherent regularities and patterns within data, which well describes data "normality". Abnormal degrees of testing instances are obtained by measuring whether they fit these learned patterns. Extensive experiments show that our approach leads to significant improvement over state-of-the-art generative/contrastive anomaly detection methods.

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. Such models have shown interesting properties, e.g., the maximum likelihood estimator exists with as little as two observations in the case of M-matrices, and exists even with one observation in the case of diagonally dominant M-matrices. We propose an adaptive multiple-stage estimation method, which refines the estimate by solving a weighted $\ell_1$-regularized problem in each stage. We further design a unified framework based on gradient projection method to solve the regularized problem, equipped with different projections to handle the constraints of M-matrices and diagonally dominant M-matrices. Theoretical analysis of the estimation error is established. The proposed method outperforms state-of-the-art methods in estimating precision matrices and identifying graph edges, as evidenced by synthetic and financial time-series data sets.

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates by incorrectly assuming flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmo- spheric dynamics, and demonstrate stable autoregressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change.

We present CTreeOT, a convergent, differentiable algorithm for matching two trees when each tree is conditioned on some input. Such conditional tree matching is useful for light-weight, few-shot adaptation of tree prediction models without parameter fine-tuning. CTreeOT includes an alignment algorithm that extends the popular Sinkhorn algorithm for matching tree nodes while supporting constraints on tree edges. The algorithm involves alternating between matrix rescaling and message passing updates, and can be efficiently expressed as GPU tensor operations. The second part of CTreeOT is fine-grained relevance-based reweighting of nodes that makes the match scores useful for prediction tasks. We demonstrate the usefulness of CTreeOT for cross-schema adaptation of Text-to-SQL, a popular semantic parsing task. We show that compared to state-of-the-art methods, we achieve significant increase in adaptation accuracy.

In domain generalization (DG), the target domain is unknown when the model is being trained, and the trained model should successfully work on an arbitrary (and possibly unseen) target domain during inference. This is a difficult problem, and despite active studies in recent years, it remains a great challenge. In this paper, we take a simple yet effective approach to tackle this issue. We propose test-time style shifting, which shifts the style of the test sample (that has a large style gap with the source domains) to the nearest source domain that the model is already familiar with, before making the prediction. This strategy enables the model to handle any target domains with arbitrary style statistics, without additional model update at test-time. Additionally, we propose style balancing, which provides a great platform for maximizing the advantage of test-time style shifting by handling the DG-specific imbalance issues. The proposed ideas are easy to implement and successfully work in conjunction with various other DG schemes. Experimental results on different datasets show the effectiveness of our methods.