The representation learning problem in the oil & gas industry aims to construct a model that provides a representation based on logging data for a well interval. Previous attempts are mainly supervised and focus on similarity task, which estimates closeness between intervals. We desire to build informative representations without using supervised (labelled) data. One of the possible approaches is self-supervised learning (SSL). In contrast to the supervised paradigm, this one requires little or no labels for the data. Nowadays, most SSL approaches are either contrastive or non-contrastive. Contrastive methods make representations of similar (positive) objects closer and distancing different (negative) ones. Due to possible wrong marking of positive and negative pairs, these methods can provide an inferior performance. Non-contrastive methods don't rely on such labelling and are widespread in computer vision. They learn using only pairs of similar objects that are easier to identify in logging data. We are the first to introduce non-contrastive SSL for well-logging data. In particular, we exploit Bootstrap Your Own Latent (BYOL) and Barlow Twins methods that avoid using negative pairs and focus only on matching positive pairs. The crucial part of these methods is an augmentation strategy. Our augmentation strategies and adaption of BYOL and Barlow Twins together allow us to achieve superior quality on clusterization and mostly the best performance on different classification tasks. Our results prove the usefulness of the proposed non-contrastive self-supervised approaches for representation learning and interval similarity in particular.

In recent years, hashing methods have been popular in the large-scale media search for low storage and strong representation capabilities. To describe objects with similar overall appearance but subtle differences, more and more studies focus on hashing-based fine-grained image retrieval. Existing hashing networks usually generate both local and global features through attention guidance on the same deep activation tensor, which limits the diversity of feature representations. To handle this limitation, we substitute convolutional descriptors for attention-guided features and propose an Attributes Grouping and Mining Hashing (AGMH), which groups and embeds the category-specific visual attributes in multiple descriptors to generate a comprehensive feature representation for efficient fine-grained image retrieval. Specifically, an Attention Dispersion Loss (ADL) is designed to force the descriptors to attend to various local regions and capture diverse subtle details. Moreover, we propose a Stepwise Interactive External Attention (SIEA) to mine critical attributes in each descriptor and construct correlations between fine-grained attributes and objects. The attention mechanism is dedicated to learning discrete attributes, which will not cost additional computations in hash codes generation. Finally, the compact binary codes are learned by preserving pairwise similarities. Experimental results demonstrate that AGMH consistently yields the best performance against state-of-the-art methods on fine-grained benchmark datasets.

While there is abundant work on methodology, algorithms, and applications, a smaller body of literature has investigated the relationship between the clusters found by a method and the underlying data-generating mechanism. Assuming that the observed data set is generated by independent and identical observations from a probability law P, consistency concerns the relationship between P and the outcome of a method for random samples of a size converging to infinity. In cluster analysis, the clustering itself and/or distributional parameters characterising the clustering may be of interest. Here we will derive consistency results for model-based clustering, i.e., clustering based on probability mixture models. More precisely, the results will concern maximum likelihood (ML) estimators (MLE) of finite mixtures of distributions from elliptically symmetrical distribution (ESD) families such as the Gaussian distribution. Finite mixture models (FMM) are convex combinations of probability distributions suitable to represent inhomogeneous populations.

We consider inverse problems where the conditional distribution of the observation ${\bf y}$ given the latent variable of interest ${\bf x}$ (also known as the forward model) is known, and we have access to a data set in which multiple instances of ${\bf x}$ and ${\bf y}$ are both observed. In this context, algorithm unrolling has become a very popular approach for designing state-of-the-art deep neural network architectures that effectively exploit the forward model. We analyze the statistical complexity of the gradient descent network (GDN), an algorithm unrolling architecture driven by proximal gradient descent. We show that the unrolling depth needed for the optimal statistical performance of GDNs is of order $\log(n)/\log(\varrho_n^{-1})$, where $n$ is the sample size, and $\varrho_n$ is the convergence rate of the corresponding gradient descent algorithm. We also show that when the negative log-density of the latent variable ${\bf x}$ has a simple proximal operator, then a GDN unrolled at depth $D'$ can solve the inverse problem at the parametric rate $O(D'/\sqrt{n})$. Our results thus also suggest that algorithm unrolling models are prone to overfitting as the unrolling depth $D'$ increases. We provide several examples to illustrate these results.

Detecting anomalies in a daily time series with a weekly pattern is a common task with a wide range of applications. A typical way of performing the task is by using decomposition method. However, the method often generates false positive results where a data point falls within its weekly range but is just off from its weekday position. We refer to this type of anomalies as "in-season anomalies", and propose a k-parameter approach to address the issue. The approach provides configurable extra tolerance for in-season anomalies to suppress misleading alerts while preserving real positives. It yields favorable result.

Online continual learning is a challenging problem where models must learn from a non-stationary data stream while avoiding catastrophic forgetting. Inter-class imbalance during training has been identified as a major cause of forgetting, leading to model prediction bias towards recently learned classes. In this paper, we theoretically analyze that inter-class imbalance is entirely attributed to imbalanced class-priors, and the function learned from intra-class intrinsic distributions is the Bayes-optimal classifier. To that end, we present that a simple adjustment of model logits during training can effectively resist prior class bias and pursue the corresponding Bayes-optimum. Our proposed method, Logit Adjusted Softmax, can mitigate the impact of inter-class imbalance not only in class-incremental but also in realistic general setups, with little additional computational cost. We evaluate our approach on various benchmarks and demonstrate significant performance improvements compared to prior arts. For example, our approach improves the best baseline by 4.6% on CIFAR10.

Representational limits of message-passing graph neural networks (MP-GNNs), e.g., in terms of the Weisfeiler-Leman (WL) test for isomorphism, are well understood. Augmenting these graph models with topological features via persistent homology (PH) has gained prominence, but identifying the class of attributed graphs that PH can recognize remains open. We introduce a novel concept of color-separating sets to provide a complete resolution to this important problem. Specifically, we establish the necessary and sufficient conditions for distinguishing graphs based on the persistence of their connected components, obtained from filter functions on vertex and edge colors. Our constructions expose the limits of vertex- and edge-level PH, proving that neither category subsumes the other. Leveraging these theoretical insights, we propose RePHINE for learning topological features on graphs. RePHINE efficiently combines vertex- and edge-level PH, achieving a scheme that is provably more powerful than both. Integrating RePHINE into MP-GNNs boosts their expressive power, resulting in gains over standard PH on several benchmarks for graph classification.

Learning the causes of time-series data is a fundamental task in many applications, spanning from finance to earth sciences or bio-medical applications. Common approaches for this task are based on vector auto-regression, and they do not take into account unknown confounding between potential causes. However, in settings with many potential causes and noisy data, these approaches may be substantially biased. Furthermore, potential causes may be correlated in practical applications. Moreover, existing algorithms often do not work with cyclic data. To address these challenges, we propose a new doubly robust method for Structure Identification from Temporal Data ( SITD ). We provide theoretical guarantees, showing that our method asymptotically recovers the true underlying causal structure. Our analysis extends to cases where the potential causes have cycles and they may be confounded. We further perform extensive experiments to showcase the superior performance of our method.

Federated Learning (FL) typically aggregates client model parameters using a weighting approach determined by sample proportions. However, this naive weighting method may lead to unfairness and degradation in model performance due to statistical heterogeneity and the inclusion of noisy data among clients. Theoretically, distributional robustness analysis has shown that the generalization performance of a learning model with respect to any shifted distribution is bounded. This motivates us to reconsider the weighting approach in federated learning. In this paper, we replace the aforementioned weighting method with a new strategy that considers the generalization bounds of each local model. Specifically, we estimate the upper and lower bounds of the second-order origin moment of the shifted distribution for the current local model, and then use these bounds disagreements as the aggregation proportions for weightings in each communication round. Experiments demonstrate that the proposed weighting strategy significantly improves the performance of several representative FL algorithms on benchmark datasets.

Federated Learning (FL) is an emerging collaborative machine learning framework where multiple clients train the global model without sharing their own datasets. In FL, the model inconsistency caused by the local data heterogeneity across clients results in the near-orthogonality of client updates, which leads to the global update norm reduction and slows down the convergence. Most previous works focus on eliminating the difference of parameters (or gradients) between the local and global models, which may fail to reflect the model inconsistency due to the complex structure of the machine learning model and the Euclidean space's limitation in meaningful geometric representations. In this paper, we propose FedMRUR by adopting the manifold model fusion scheme and a new global optimizer to alleviate the negative impacts. Concretely, FedMRUR adopts a hyperbolic graph manifold regularizer enforcing the representations of the data in the local and global models are close to each other in a low-dimensional subspace. Because the machine learning model has the graph structure, the distance in hyperbolic space can reflect the model bias better than the Euclidean distance. In this way, FedMRUR exploits the manifold structures of the representations to significantly reduce the model inconsistency. FedMRUR also aggregates the client updates norms as the global update norm, which can appropriately enlarge each client's contribution to the global update, thereby mitigating the norm reduction introduced by the near-orthogonality of client updates. Furthermore, we theoretically prove that our algorithm can achieve a linear speedup property for non-convex setting under partial client participation.Experiments demonstrate that FedMRUR can achieve a new state-of-the-art (SOTA) accuracy with less communication.