Time series with missing or irregularly sampled data are a persistent challenge in machine learning. Many methods operate on the frequency-domain, relying on the Fast Fourier Transform (FFT) which assumes uniform sampling, therefore requiring prior interpolation that can distort the spectra. To address this limitation, we introduce a differentiable Lomb–Scargle layer that enables a reliable computation of the power spectrum of irregularly sampled data. We integrate this layer into a novel score-based diffusion model (LSCD) for time series imputation conditioned on the entire signal spectrum. Experiments on synthetic and real-world benchmarks demonstrate that our method recovers missing data more accurately than purely time-domain baselines, while simultaneously producing consistent frequency estimates. Crucially, our method can be easily integrated into learning frameworks, enabling broader adoption of spectral guidance in machine learning approaches involving incomplete or irregular data.

While financial data presents one of the most challenging and interesting sequence modelling tasks due to high noise, heavy tails, and strategic interactions, progress in this area has been hindered by the lack of consensus on quantitative evaluation paradigms. To address this, we present LOB-Bench, a benchmark, implemented in python, designed to evaluate the quality and realism of generative message-by-order data for limit order books (LOB) in the LOBSTER format. Our framework measures distributional differences in conditional and unconditional statistics between generated and real LOB data, supporting flexible multivariate statistical evaluation. The benchmark also includes features commonly used LOB statistics such as spread, order book volumes, order imbalance, and message inter-arrival times, along with scores from a trained discriminator network. Lastly, LOB-Bench contains "market impact metrics", i.e. the cross-correlations and price response functions for specific events in the data. We benchmark generative autoregressive state-space models, a (C)GAN, as well as a parametric LOB model and find that the autoregressive GenAI approach beats traditional model classes.

In recent years, mixup regularization has gained popularity as an effective way to improve the generalization performance of deep learning models by training on convex combinations of training data. While many mixup variants have been explored, the proper adoption of the technique to conditional density estimation and probabilistic machine learning remains relatively unexplored. This work introduces a novel framework for mixup regularization based on probabilistic fusion that is better suited for conditional density estimation tasks. For data distributed according to a member of the exponential family, we show that likelihood functions can be analytically fused using log-linear pooling. We further propose an extension of probabilistic mixup, which allows for fusion of inputs at an arbitrary intermediate layer of the neural network. We provide a theoretical analysis comparing our approach to standard mixup variants. Empirical results on synthetic and real datasets demonstrate the benefits of our proposed framework compared to existing mixup variants.

Large Language Models (LLMs) offer the potential for automatic time series analysis and reporting, which is a critical task across many domains, spanning healthcare, finance, climate, energy, and many more.In this paper, we propose a framework for rigorously evaluating the capabilities of LLMs on time series understanding, encompassing both univariate and multivariate forms.We introduce a comprehensive taxonomy of time series features, a critical framework that delineates various characteristics inherent in time series data.Leveraging this taxonomy, we have systematically designed and synthesized a diverse dataset of time series, embodying the different outlined features, each accompanied by textual descriptions.This dataset acts as a solid foundation for assessing the proficiency of LLMs in comprehending time series.Our experiments shed light on the strengths and limitations of stateof-the-art LLMs in time series understanding, revealing which features these models readily comprehend effectively and where they falter.In addition, we uncover the sensitivity of LLMs to factors including the formatting of the data, the position of points queried within a series and the overall time series length.Table 1: Taxonomy of time series characteristics.

Data augmentation techniques play an important role in enhancing the performance of deep learning models. Despite their proven benefits in computer vision tasks, their application in the other domains remains limited. This paper proposes a Mixup regularization scheme, referred to as UMAP Mixup, designed for "on-manifold" automated data augmentation for deep learning predictive models. The proposed approach ensures that the Mixup operations result in synthesized samples that lie on the data manifold of the features and labels by utilizing a dimensionality reduction technique known as uniform manifold approximation and projection. Evaluations across diverse regression tasks show that UMAP Mixup is competitive with or outperforms other Mixup variants, show promise for its potential as an effective tool for enhancing the generalization performance of deep learning models.

Stochastic differential equations (SDEs) have been widely used to model real world random phenomena. Existing works mainly focus on the case where the time series is modeled by a single SDE, which might be restrictive for modeling time series with distributional shift. In this work, we propose a change point detection algorithm for time series modeled as neural SDEs. Given a time series dataset, the proposed method jointly learns the unknown change points and the parameters of distinct neural SDE models corresponding to each change point. Specifically, the SDEs are learned under the framework of generative adversarial networks (GANs) and the change points are detected based on the output of the GAN discriminator in a forward pass. Numerical results on both synthetic and real datasets are provided to validate the performance of the algorithm in comparison to classical change point detection benchmarks, standard GAN-based neural SDEs, and other state-of-the-art deep generative models for time series data.

Learning agent behaviors from observational data has shown to improve our understanding of their decision-making processes, advancing our ability to explain their interactions with the environment and other agents. While multiple learning techniques have been proposed in the literature, there is one particular setting that has not been explored yet: multi agent systems where agent identities remain anonymous. For instance, in financial markets labeled data that identifies market participant strategies is typically proprietary, and only the anonymous state-action pairs that result from the interaction of multiple market participants are publicly available. As a result, sequences of agent actions are not observable, restricting the applicability of existing work. In this paper, we propose a Policy Clustering algorithm, called K-SHAP, that learns to group anonymous state-action pairs according to the agent policies. We frame the problem as an Imitation Learning (IL) task, and we learn a world-policy able to mimic all the agent behaviors upon different environmental states. We leverage the world-policy to explain each anonymous observation through an additive feature attribution method called SHAP (SHapley Additive exPlanations). Finally, by clustering the explanations we show that we are able to identify different agent policies and group observations accordingly. We evaluate our approach on simulated synthetic market data and a real-world financial dataset. We show that our proposal significantly and consistently outperforms the existing methods, identifying different agent strategies.

Synthetic time series are often used in practical applications to augment the historical time series dataset, amplify the occurrence of rare events and also create counterfactual scenarios. Distributional-similarity (which we refer to as realism) as well as the satisfaction of certain numerical constraints are common requirements for counterfactual time series generation. For instance, the US Federal Reserve publishes synthetic market stress scenarios given by the constrained time series for financial institutions to assess their performance in hypothetical recessions. Existing approaches for generating constrained time series usually penalize training loss to enforce constraints, and reject non-conforming samples. However, these approaches would require re-training if we change constraints, and rejection sampling can be computationally expensive, or impractical for complex constraints. In this paper, we propose a novel set of methods to tackle the constrained time series generation problem and provide efficient sampling while ensuring the realism of generated time series. In particular, we frame the problem using a constrained optimization framework and then we propose a set of generative methods including 'GuidedDiffTime', a guided diffusion model. We empirically evaluate our work on several datasets for financial and energy data, where incorporating constraints is critical. We show that our approaches outperform existing work both qualitatively and quantitatively, and that 'GuidedDiffTime' does not require re-training for new constraints, resulting in a significant carbon footprint reduction, up to 92% w.r.t. existing deep learning methods.

This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs), which enables accurate quantification of both epistemic and aleatoric uncertainty. By assuming the data generating process follows that of a Gaussian mixture, DGMEs are capable of approximating complex probability distributions, such as heavy-tailed or multimodal distributions. Our contributions include the derivation of an expectation-maximization (EM) algorithm used for learning the model parameters, which results in an upper-bound on the log-likelihood of training data over that of standard deep ensembles. Additionally, the proposed EM training procedure allows for learning of mixture weights, which is not commonly done in ensembles. Our experimental results demonstrate that DGMEs outperform state-of-the-art uncertainty quantifying deep learning models in handling complex predictive densities.

Random linear network codes can be designed and implemented in a distributed manner, with low computational complexity. However, these codes are classically implemented over finite fields whose size depends on some global network parameters (size of the network, the number of sinks) that may be unknown prior to code design. Also, the entire network code may have to be redesigned when a new node joins. In this work, we present the first universal and robust distributed linear network coding schemes. Our schemes are universal since they are independent of all network parameters. They are robust since in case nodes join or leave, the remaining nodes do not need to change their coding operations and the receivers can still decode. They are distributed since nodes need only have topological information about the part of the network upstream of them, which can be naturally streamed as part of the communication protocol. We present both probabilistic and deterministic schemes that are all asymptotically rate-optimal in the coding block-length, and have guarantees of correctness. Our probabilistic designs are computationally efficient, with order-optimal complexity. Our deterministic designs guarantee zero error decoding, albeit via codes with high computational complexity in general. Our coding schemes are based on network codes over “scalable fields”. Instead of choosing coding coefficients from one field at every node as in, each node uses linear coding operations over an “effective field-size” which depends on the node's distance from the source node. The analysis of our schemes requires technical tools that may be of independent interest. In particular, we generalize the Schwartz-Zippel lemma by proving a nonuniform version, wherein variables are chosen from sets of possibly different sizes. We also provide a novel robust distributed algorithm to assign unique IDs to network nodes.

This work considers the multiple-access multicast error-correction scenario over a packetized network withzmalicious edge adversaries. The network has min-cutmand packets of lengthl, and each sink demands all information from the set of sourcesS. The capacity region is characterized for both a “side-channel” model (where sources and sinks share some random bits that are secret from the adversary) and an “omniscient” adversarial model (where no limitations on the adversary's knowledge are assumed). In the “side-channel” adversarial model, the use of a secret channel allows higher rates to be achieved compared to the “omniscient” adversarial model, and a polynomial-complexity capacity-achieving code is provided. For the “omniscient” adversarial model, two capacity-achieving constructions are given: the first is based on random subspace code design and has complexity exponential inlm, while the second uses a novel multiple-field-extension technique and has O(lm|S|) complexity, which is polynomial in the network size. Our code constructions are “end-to-end” in that all nodes except the sources and sinks are oblivious to the adversaries and may simply implement predesigned linear network codes (random or otherwise). Also, the sources act independently without knowledge of the data from other sources.

We consider the problem of correcting errors and erasures with network coding. Unlike existing works which consider performance limits for worst-case locations of given numbers of errors and erasures, we consider the performance of given (not necessarily optimal) coding and forwarding strategies for given (not necessarily worst-case) models of error and erasure locations. Our approach characterizes decoding success in terms of the rank of certain matrices corresponding to useful and erroneous information received at the sink nodes. We use this approach to analyze random coding and forwarding strategies on a family of simple networks with random error and erasure locations, and show that the relative performance of the strategies depends on the erasure and error probabilities.

In this paper we derive capacity regions for network error correction with both known and unknown topologies (coherent and non-coherent network coding) under a multiple-source multicast transmission scenario. For the multiple-source non-multicast scenario, given any achievable network code for the error-free case, we construct a code with a reduced rate region for the case with errors.