Common practice in modern machine learning involves fitting a large number of parameters relative to the number of observations. These overparameterized models can exhibit surprising generalization behavior, e.g., ``double descent'' in the prediction error curve when plotted against the raw number of model parameters, or another simplistic notion of complexity. In this paper, we revisit model complexity from first principles, by first reinterpreting and then extending the classical statistical concept of (effective) degrees of freedom. Whereas the classical definition is connected to fixed-X prediction error (in which prediction error is defined by averaging over the same, nonrandom covariate points as those used during training), our extension of degrees of freedom is connected to random-X prediction error (in which prediction error is averaged over a new, random sample from the covariate distribution). The random-X setting more naturally embodies modern machine learning problems, where highly complex models, even those complex enough to interpolate the training data, can still lead to desirable generalization performance under appropriate conditions. We demonstrate the utility of our proposed complexity measures through a mix of conceptual arguments, theory, and experiments, and illustrate how they can be used to interpret and compare arbitrary prediction models.

Previously, we showed that computational mechanic's causal states -- predictively-equivalent trajectory classes for a stochastic dynamical system -- can be cast into a reproducing kernel Hilbert space. The result is a widely-applicable method that infers causal structure directly from very different kinds of observations and systems. Here, we expand this method to explicitly introduce the causal diffusion components it produces. These encode the kernel causal-state estimates as a set of coordinates in a reduced dimension space. We show how each component extracts predictive features from data and demonstrate their application on four examples: first, a simple pendulum -- an exactly solvable system; second, a molecular-dynamic trajectory of $n$-butane -- a high-dimensional system with a well-studied energy landscape; third, the monthly sunspot sequence -- the longest-running available time series of direct observations; and fourth, multi-year observations of an active crop field -- a set of heterogeneous observations of the same ecosystem taken for over a decade. In this way, we demonstrate that the empirical kernel causal-states algorithm robustly discovers predictive structures for systems with widely varying dimensionality and stochasticity.

Geological Carbon Storage GCS is arguably the only scalable net-negative CO2 emission technology available While promising subsurface complexities and heterogeneity of reservoir properties demand a systematic approach to quantify uncertainty when optimizing production and mitigating storage risks which include assurances of Containment and Conformance of injected supercritical CO2 As a first step towards the design and implementation of a Digital Twin for monitoring underground storage operations a machine learning based data-assimilation framework is introduced and validated on carefully designed realistic numerical simulations As our implementation is based on Bayesian inference but does not yet support control and decision-making we coin our approach an uncertainty-aware Digital Shadow To characterize the posterior distribution for the state of CO2 plumes conditioned on multi-modal time-lapse data the envisioned Shadow combines techniques from Simulation-Based Inference SBI and Ensemble Bayesian Filtering to establish probabilistic baselines and assimilate multi-modal data for GCS problems that are challenged by large degrees of freedom nonlinear multi-physics non-Gaussianity and computationally expensive to evaluate fluid flow and seismic simulations To enable SBI for dynamic systems a recursive scheme is proposed where the Digital Shadows neural networks are trained on simulated ensembles for their state and observed data well and/or seismic Once training is completed the systems state is inferred when time-lapse field data becomes available In this computational study we observe that a lack of knowledge on the permeability field can be factored into the Digital Shadows uncertainty quantification To our knowledge this work represents the first proof of concept of an uncertainty-aware in-principle scalable Digital Shadow.

In this work, three fundamentally different machine learning models are combined to create a new, joint model for forecasting the UEFA EURO 2024. Therefore, a generalized linear model, a random forest model, and a extreme gradient boosting model are used to predict the number of goals a team scores in a match. The three models are trained on the match results of the UEFA EUROs 2004-2020, with additional covariates characterizing the teams for each tournament as well as three enhanced variables derived from different ranking methods for football teams. The first enhanced variable is based on historic match data from national teams, the second is based on the bookmakers' tournament winning odds of all participating teams, and the third is based on historic match data of individual players both for club and international matches, resulting in player ratings. Then, based on current covariate information of the participating teams, the final trained model is used to predict the UEFA EURO 2024. For this purpose, the tournament is simulated 100.000 times, based on the estimated expected number of goals for all possible matches, from which probabilities across the different tournament stages are derived. Our combined model identifies France as the clear favourite with a winning probability of 19.2%, followed by England (16.7%) and host Germany (13.7%).

Detecting credit card fraud (CCF) holds significant importance due to its role in safeguarding consumers from unauthorized transactions that have the potential to result in financial detriment and negative impacts on their credit rating. It aids financial institutions in upholding the reliability of their payment mechanisms and circumventing the expensive procedure of compensating for deceitful transactions. The utilization of Artificial Intelligence methodologies demonstrated remarkable efficacy in the identification of credit card fraud instances. Within this study, we present a unique attention-based ensemble model. This model is enhanced by adding an attention layer for integration of first layer classifiers' predictions and a selection layer for choosing the best integrated value. The attention layer is implemented with two aggregation operators: dependent ordered weighted averaging (DOWA) and induced ordered weighted averaging (IOWA). The performance of the IOWA operator is very close to the learning algorithm in neural networks which is based on the gradient descent optimization method, and performing the DOWA operator is based on weakening the classifiers that make outlier predictions compared to other learners. Both operators have a sufficient level of complexity for the recognition of complex patterns. Accuracy and diversity are the two criteria we use for selecting the classifiers whose predictions are to be integrated by the two aggregation operators. Using a bootstrap forest, we identify the 13 most significant features of the dataset that contribute the most to CCF detection and use them to feed the proposed model. Exhibiting its efficacy, the ensemble model attains an accuracy of 99.95% with an area under the curve (AUC) of 1.

Gene regulation is a dynamic process that underlies all aspects of human development, disease response, and other key biological processes. The reconstruction of temporal gene regulatory networks has conventionally relied on regression analysis, graphical models, or other types of relevance networks. With the large increase in time series single-cell data, new approaches are needed to address the unique scale and nature of this data for reconstructing such networks. Here, we develop a deep neural network, Marlene, to infer dynamic graphs from time series single-cell gene expression data. Marlene constructs directed gene networks using a self-attention mechanism where the weights evolve over time using recurrent units. By employing meta learning, the model is able to recover accurate temporal networks even for rare cell types. In addition, Marlene can identify gene interactions relevant to specific biological responses, including COVID-19 immune response, fibrosis, and aging. Biological systems are dynamic, changing over time in response to various stimuli and events. To construct accurate models of biological activity during development, disease progression, treatment response, and other biological processes, it is essential to track their evolution over time (Bar-Joseph et al., 2012). Studying the regulation of these dynamic processes is key for understanding the underlying mechanisms that drive the response and for identifying potential interventions that can serve as cures for diseases (Silverman et al., 2020). Much of the research in this area is focused on the reconstruction of regulatory networks (Karlebach & Shamir, 2008; Badia-I-Mompel et al., 2023).

Monkeypox (MPox) has emerged as a significant global concern, with cases steadily increasing daily. Conventional detection methods, including polymerase chain reaction (PCR) and manual examination, exhibit challenges of low sensitivity, high cost, and substantial workload. Therefore, deep learning offers an automated solution; however, the datasets include data scarcity, texture, contrast, inter-intra class variability, and similarities with other skin infectious diseases. In this regard, a novel hybrid approach is proposed that integrates the learning capacity of Residual Learning and Spatial Exploitation Convolutional Neural Network (CNN) with a customized Swin Transformer (RS-FME-SwinT) to capture multi-scale global and local correlated features for MPox diagnosis. The proposed RS-FME-SwinT technique employs a transfer learning-based feature map enhancement (FME) technique, integrating the customized SwinT for global information capture, residual blocks for texture extraction, and spatial blocks for local contrast variations. Moreover, incorporating new inverse residual blocks within the proposed SwinT effectively captures local patterns and mitigates vanishing gradients. The proposed RS-FME-SwinT has strong learning potential of diverse features that systematically reduce intra-class MPox variation and enable precise discrimination from other skin diseases. Finally, the proposed RS-FME-SwinT is a holdout cross-validated on a diverse MPox dataset and achieved outperformance on state-of-the-art CNNs and ViTs. The proposed RS-FME-SwinT demonstrates commendable results of an accuracy of 97.80%, sensitivity of 96.82%, precision of 98.06%, and an F-score of 97.44% in MPox detection. The RS-FME-SwinT could be a valuable tool for healthcare practitioners, enabling prompt and accurate MPox diagnosis and contributing significantly to mitigation efforts.

In cross-device federated learning (FL) with millions of mobile clients, only a small subset of clients participate in training in every communication round, and Federated Averaging (FedAvg) is the most popular algorithm in practice. Existing analyses of FedAvg usually assume the participating clients are independently sampled in each round from a uniform distribution, which does not reflect real-world scenarios. This paper introduces a theoretical framework that models client participation in FL as a Markov chain to study optimization convergence when clients have non-uniform and correlated participation across rounds. We apply this framework to analyze a more general and practical pattern: every client must wait a minimum number of $R$ rounds (minimum separation) before re-participating. We theoretically prove and empirically observe that increasing minimum separation reduces the bias induced by intrinsic non-uniformity of client availability in cross-device FL systems. Furthermore, we develop an effective debiasing algorithm for FedAvg that provably converges to the unbiased optimal solution under arbitrary minimum separation and unknown client availability distribution.

Stochastic gradient descent (SGD) is a powerful optimization technique that is particularly useful in online learning scenarios. Its convergence analysis is relatively well understood under the assumption that the data samples are independent and identically distributed (iid). However, applying SGD to policy optimization problems in operations research involves a distinct challenge: the policy changes the environment and thereby affects the data used to update the policy. The adaptively generated data stream involves samples that are non-stationary, no longer independent from each other, and affected by previous decisions. The influence of previous decisions on the data generated introduces bias in the gradient estimate, which presents a potential source of instability for online learning not present in the iid case. In this paper, we introduce simple criteria for the adaptively generated data stream to guarantee the convergence of SGD. We show that the convergence speed of SGD with adaptive data is largely similar to the classical iid setting, as long as the mixing time of the policy-induced dynamics is factored in. Our Lyapunov-function analysis allows one to translate existing stability analysis of stochastic systems studied in operations research into convergence rates for SGD, and we demonstrate this for queueing and inventory management problems. We also showcase how our result can be applied to study the sample complexity of an actor-critic policy gradient algorithm.

We introduce ORC-ManL, a new algorithm to prune spurious edges from nearest neighbor graphs using a criterion based on Ollivier-Ricci curvature and estimated metric distortion. Our motivation comes from manifold learning: we show that when the data generating the nearest-neighbor graph consists of noisy samples from a low-dimensional manifold, edges that shortcut through the ambient space have more negative Ollivier-Ricci curvature than edges that lie along the data manifold. We demonstrate that our method outperforms alternative pruning methods and that it significantly improves performance on many downstream geometric data analysis tasks that use nearest neighbor graphs as input. Specifically, we evaluate on manifold learning, persistent homology, dimension estimation, and others. We also show that ORC-ManL can be used to improve clustering and manifold learning of single-cell RNA sequencing data. Finally, we provide empirical convergence experiments that support our theoretical findings.