Conformal Prediction (CP) algorithms estimate the uncertainty of a prediction model by calibrating its outputs on labeled data. The same calibration scheme usually applies to any model and data without modifications. The obtained prediction intervals are valid by construction but could be inefficient, i.e. unnecessarily big, if the prediction errors are not uniformly distributed over the input space. We present a general scheme to localize the intervals by training the calibration process. The standard prediction error is replaced by an optimized distance metric that depends explicitly on the object attributes. Learning the optimal metric is equivalent to training a Normalizing Flow that acts on the joint distribution of the errors and the inputs. Unlike the Error Reweighting CP algorithm of Papadopoulos et al. (2008), the framework allows estimating the gap between nominal and empirical conditional validity. The approach is compatible with existing locally-adaptive CP strategies based on re-weighting the calibration samples and applies to any point-prediction model without retraining.

This paper presents a succinct derivation of the training and generalization performance of a variety of high-dimensional ridge regression models using the basic tools of random matrix theory and free probability. We provide an introduction and review of recent results on these topics, aimed at readers with backgrounds in physics and deep learning. Analytic formulas for the training and generalization errors are obtained in a few lines of algebra directly from the properties of the $S$-transform of free probability. This allows for a straightforward identification of the sources of power-law scaling in model performance. We compute the generalization error of a broad class of random feature models. We find that in all models, the $S$-transform corresponds to the train-test generalization gap, and yields an analogue of the generalized-cross-validation estimator. Using these techniques, we derive fine-grained bias-variance decompositions for a very general class of random feature models with structured covariates. These novel results allow us to discover a scaling regime for random feature models where the variance due to the features limits performance in the overparameterized setting. We also demonstrate how anisotropic weight structure in random feature models can limit performance and lead to nontrivial exponents for finite-width corrections in the overparameterized setting. Our results extend and provide a unifying perspective on earlier models of neural scaling laws.

Exact computation of various machine learning explanations requires numerous model evaluations and in extreme cases becomes impractical. The computational cost of approximation increases with an ever-increasing size of data and model parameters. Many heuristics have been proposed to approximate post-hoc explanations efficiently. This paper shows that the standard i.i.d. sampling used in a broad spectrum of algorithms for explanation estimation leads to an approximation error worthy of improvement. To this end, we introduce Compress Then Explain (CTE), a new paradigm for more efficient and accurate explanation estimation. CTE uses distribution compression through kernel thinning to obtain a data sample that best approximates the marginal distribution. We show that CTE improves the estimation of removal-based local and global explanations with negligible computational overhead. It often achieves an on-par explanation approximation error using 2-3x less samples, i.e. requiring 2-3x less model evaluations. CTE is a simple, yet powerful, plug-in for any explanation method that now relies on i.i.d. sampling.

DBSCAN and OPTICS are powerful algorithms for identifying clusters of points in domains where few assumptions can be made about the structure of the data. In this paper, we leverage these strengths and introduce a new algorithm, LINSCAN, designed to seek lineated clusters that are difficult to find and isolate with existing methods. In particular, by embedding points as normal distributions approximating their local neighborhoods and leveraging a distance function derived from the Kullback Leibler Divergence, LINSCAN can detect and distinguish lineated clusters that are spatially close but have orthogonal covariances. We demonstrate how LINSCAN can be applied to seismic data to identify active faults, including intersecting faults, and determine their orientation. Finally, we discuss the properties a generalization of DBSCAN and OPTICS must have in order to retain the stability benefits of these algorithms.

Long-term stability stands as a crucial requirement in data-driven medium-range global weather forecasting. Spectral bias is recognized as the primary contributor to instabilities, as data-driven methods difficult to learn small-scale dynamics. In this paper, we reveal that the universal mechanism for these instabilities is not only related to spectral bias but also to distortions brought by processing spherical data using conventional convolution. These distortions lead to a rapid amplification of errors over successive long-term iterations, resulting in a significant decline in forecast accuracy. To address this issue, a universal neural operator called the Spherical Harmonic Neural Operator (SHNO) is introduced to improve long-term iterative forecasts. SHNO uses the spherical harmonic basis to mitigate distortions for spherical data and uses gated residual spectral attention (GRSA) to correct spectral bias caused by spurious correlations across different scales. The effectiveness and merit of the proposed method have been validated through its application for spherical Shallow Water Equations (SWEs) and medium-range global weather forecasting. Our findings highlight the benefits and potential of SHNO to improve the accuracy of long-term prediction.

Depression recognition based on physiological signals such as functional near-infrared spectroscopy (fNIRS) and electroencephalogram (EEG) has made considerable progress. However, most existing studies ignore the complementarity and semantic consistency of multimodal physiological signals under the same stimulation task in complex spatio-temporal patterns. In this paper, we introduce a multimodal physiological signals representation learning framework using Siamese architecture via multiscale contrasting for depression recognition (MRLMC). First, fNIRS and EEG are transformed into different but correlated data based on a time-domain data augmentation strategy. Then, we design a spatio-temporal contrasting module to learn the representation of fNIRS and EEG through weight-sharing multiscale spatio-temporal convolution. Furthermore, to enhance the learning of semantic representation associated with stimulation tasks, a semantic consistency contrast module is proposed, aiming to maximize the semantic similarity of fNIRS and EEG. Extensive experiments on publicly available and self-collected multimodal physiological signals datasets indicate that MRLMC outperforms the state-of-the-art models. Moreover, our proposed framework is capable of transferring to multimodal time series downstream tasks.

The Balanced-Pairwise-Affinities (BPA) feature transform is designed to upgrade the features of a set of input items to facilitate downstream matching or grouping related tasks. The transformed set encodes a rich representation of high order relations between the input features. A particular min-cost-max-flow fractional matching problem, whose entropy regularized version can be approximated by an optimal transport (OT) optimization, leads to a transform which is efficient, differentiable, equivariant, parameterless and probabilistically interpretable. While the Sinkhorn OT solver has been adapted extensively in many contexts, we use it differently by minimizing the cost between a set of features to $itself$ and using the transport plan's $rows$ as the new representation. Empirically, the transform is highly effective and flexible in its use and consistently improves networks it is inserted into, in a variety of tasks and training schemes. We demonstrate state-of-the-art results in few-shot classification, unsupervised image clustering and person re-identification. Code is available at \url{github.com/DanielShalam/BPA}.

In settings where only a budgeted amount of labeled data can be afforded, active learning seeks to devise query strategies for selecting the most informative data points to be labeled, aiming to enhance learning algorithms' efficiency and performance. Numerous such query strategies have been proposed and compared in the active learning literature. However, the community still lacks standardized benchmarks for comparing the performance of different query strategies. This particularly holds for the combination of query strategies with different learning algorithms into active learning pipelines and examining the impact of the learning algorithm choice. To close this gap, we propose ALPBench, which facilitates the specification, execution, and performance monitoring of active learning pipelines. It has built-in measures to ensure evaluations are done reproducibly, saving exact dataset splits and hyperparameter settings of used algorithms. In total, ALPBench consists of 86 real-world tabular classification datasets and 5 active learning settings, yielding 430 active learning problems. To demonstrate its usefulness and broad compatibility with various learning algorithms and query strategies, we conduct an exemplary study evaluating 9 query strategies paired with 8 learning algorithms in 2 different settings.

In this paper, we propose a scalable community detection algorithm using hypergraph modularity function, h-Louvain. It is an adaptation of the classical Louvain algorithm in the context of hypergraphs. We observe that a direct application of the Louvain algorithm to optimize the hypergraph modularity function often fails to find meaningful communities. We propose a solution to this issue by adjusting the initial stage of the algorithm via carefully and dynamically tuned linear combination of the graph modularity function of the corresponding two-section graph and the desired hypergraph modularity function. The process is guided by Bayesian optimization of the hyper-parameters of the proposed procedure. Various experiments on synthetic as well as real-world networks are performed showing that this process yields improved results in various regimes.

Recent efforts to scale Transformer models have demonstrated rapid progress across a wide range of tasks (Wei et al., 2022). However, fine-tuning these models for downstream tasks is expensive due to their large parameter counts. Parameter-efficient fine-tuning (PEFT) approaches have emerged as a viable alternative by allowing us to fine-tune models by updating only a small number of parameters. In this work, we propose a general framework for parameter efficient fine-tuning (PEFT), based on structured unrestricted-rank matrices (SURM) which can serve as a drop-in replacement for popular approaches such as Adapters and LoRA. Unlike other methods like LoRA, SURMs provides more flexibility in finding the right balance between compactness and expressiveness. This is achieved by using low displacement rank matrices (LDRMs), which hasn't been used in this context before. SURMs remain competitive with baselines, often providing significant quality improvements while using a smaller parameter budget. SURMs achieve 5-7% accuracy gains on various image classification tasks while replacing low-rank matrices in LoRA. It also results in up to 12x reduction of the number of parameters in adapters (with virtually no loss in quality) on the GLUE benchmark.