Yousef El-Laham

Defu Cao, Yousef El-Laham, Loc Trinh et al.

In electronic trading markets, limit order books (LOBs) provide information about pending buy/sell orders at various price levels for a given security. Recently, there has been a growing interest in using LOB data for resolving downstream machine learning tasks (e.g., forecasting). However, dealing with out-of-distribution (OOD) LOB data is challenging since distributional shifts are unlabeled in current publicly available LOB datasets. Therefore, it is critical to build a synthetic LOB dataset with labeled OOD samples serving as a testbed for developing models that generalize well to unseen scenarios. In this work, we utilize a multi-agent market simulator to build a synthetic LOB dataset, named DSLOB, with and without market stress scenarios, which allows for the design of controlled distributional shift benchmarking. Using the proposed synthetic dataset, we provide a holistic analysis on the forecasting performance of three different state-of-the-art forecasting methods. Our results reflect the need for increased researcher efforts to develop algorithms with robustness to distributional shifts in high-frequency time series data.

Elizabeth Fons, Alejandro Sztrajman, Yousef El-laham et al.

Implicit neural representations (INRs) have recently emerged as a powerful tool that provides an accurate and resolution-independent encoding of data. Their robustness as general approximators has been shown in a wide variety of data sources, with applications on image, sound, and 3D scene representation. However, little attention has been given to leveraging these architectures for the representation and analysis of time series data. In this paper, we analyze the representation of time series using INRs, comparing different activation functions in terms of reconstruction accuracy and training convergence speed. We show how these networks can be leveraged for the imputation of time series, with applications on both univariate and multivariate data. Finally, we propose a hypernetwork architecture that leverages INRs to learn a compressed latent representation of an entire time series dataset. We introduce an FFT-based loss to guide training so that all frequencies are preserved in the time series. We show that this network can be used to encode time series as INRs, and their embeddings can be interpolated to generate new time series from existing ones. We evaluate our generative method by using it for data augmentation, and show that it is competitive against current state-of-the-art approaches for augmentation of time series.

Yousef El-Laham, Svitlana Vyetrenko

Neural style transfer is a powerful computer vision technique that can incorporate the artistic "style" of one image to the "content" of another. The underlying theory behind the approach relies on the assumption that the style of an image is represented by the Gram matrix of its features, which is typically extracted from pre-trained convolutional neural networks (e.g., VGG-19). This idea does not straightforwardly extend to time series stylization since notions of style for two-dimensional images are not analogous to notions of style for one-dimensional time series. In this work, a novel formulation of time series style transfer is proposed for the purpose of synthetic data generation and enhancement. We introduce the concept of stylized features for time series, which is directly related to the time series realism properties, and propose a novel stylization algorithm, called StyleTime, that uses explicit feature extraction techniques to combine the underlying content (trend) of one time series with the style (distributional properties) of another. Further, we discuss evaluation metrics, and compare our work to existing state-of-the-art time series generation and augmentation schemes. To validate the effectiveness of our methods, we use stylized synthetic data as a means for data augmentation to improve the performance of recurrent neural network models on several forecasting tasks.

Yousef El-Laham, Niccolò Dalmasso, Elizabeth Fons et al.

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.

Tom Bamford, Elizabeth Fons, Yousef El-Laham et al.

Time series imputation remains a significant challenge across many fields due to the potentially significant variability in the type of data being modelled. Whilst traditional imputation methods often impose strong assumptions on the underlying data generation process, limiting their applicability, researchers have recently begun to investigate the potential of deep learning for this task, inspired by the strong performance shown by these models in both classification and regression problems across a range of applications. In this work we propose MADS, a novel auto-decoding framework for time series imputation, built upon implicit neural representations. Our method leverages the capabilities of SIRENs for high fidelity reconstruction of signals and irregular data, and combines it with a hypernetwork architecture which allows us to generalise by learning a prior over the space of time series. We evaluate our model on two real-world datasets, and show that it outperforms state-of-the-art methods for time series imputation. On the human activity dataset, it improves imputation performance by at least 40%, while on the air quality dataset it is shown to be competitive across all metrics. When evaluated on synthetic data, our model results in the best average rank across different dataset configurations over all baselines.

Vamsi K. Potluru, Daniel Borrajo, Andrea Coletta et al.

Synthetic data has made tremendous strides in various commercial settings including finance, healthcare, and virtual reality. We present a broad overview of prototypical applications of synthetic data in the financial sector and in particular provide richer details for a few select ones. These cover a wide variety of data modalities including tabular, time-series, event-series, and unstructured arising from both markets and retail financial applications. Since finance is a highly regulated industry, synthetic data is a potential approach for dealing with issues related to privacy, fairness, and explainability. Various metrics are utilized in evaluating the quality and effectiveness of our approaches in these applications. We conclude with open directions in synthetic data in the context of the financial domain.

Yousef El-Laham, Elizabeth Fons, Dillon Daudert et al.

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.

Zhongchang Sun, Yousef El-Laham, Svitlana Vyetrenko

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. At each step of the proposed algorithm, the change points and the SDE model parameters are updated in an alternating fashion. Numerical results on both synthetic and real datasets are provided to validate the performance of our 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.

Yousef El-Laham, Zhongchang Sun, Haibei Zhu et al.

In this work, we explore modeling change points in time-series data using neural stochastic differential equations (neural SDEs). We propose a novel model formulation and training procedure based on the variational autoencoder (VAE) framework for modeling time-series as a neural SDE. Unlike existing algorithms training neural SDEs as VAEs, our proposed algorithm only necessitates a Gaussian prior of the initial state of the latent stochastic process, rather than a Wiener process prior on the entire latent stochastic process. We develop two methodologies for modeling and estimating change points in time-series data with distribution shifts. Our iterative algorithm alternates between updating neural SDE parameters and updating the change points based on either a maximum likelihood-based approach or a change point detection algorithm using the sequential likelihood ratio test. We provide a theoretical analysis of this proposed change point detection scheme. Finally, we present an empirical evaluation that demonstrates the expressive power of our proposed model, showing that it can effectively model both classical parametric SDEs and some real datasets with distribution shifts.

Kulunu Dharmakeerthi, Yousef El-Laham, Henry H. Wong et al.

Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these approaches can face significant challenges when modeling a conditional distribution, $P(Y|X=x)$, when $P(X=x)$ is small. In these regions, few samples, if any, are available for training, thus modeling the corresponding conditional density may be difficult. Recognizing this, we show it is possible to adapt the data representation and forward scheme so that the sample complexity of learning a score-based generative model is small in low probability regions of the conditioning space. Drawing inspiration from conditional extreme value theory we characterize this method precisely in the special case in the tail regions of the conditioning variable, $X$. We show how diffusion with a data-driven choice of nonlinear drift term is best suited to model tail events under an appropriate representation of the data. Through empirical validation on two synthetic datasets and a real-world financial dataset, we demonstrate that our tail-adaptive approach significantly outperforms standard diffusion models in accurately capturing response distributions at the extreme tail conditions.

Benjamin Sterling, Yousef El-Laham, Mónica F. Bugallo

Recent advances in generative artificial intelligence applications have raised new data security concerns. This paper focuses on defending diffusion models against membership inference attacks. This type of attack occurs when the attacker can determine if a certain data point was used to train the model. Although diffusion models are intrinsically more resistant to membership inference attacks than other generative models, they are still susceptible. The defense proposed here utilizes critically-damped higher-order Langevin dynamics, which introduces several auxiliary variables and a joint diffusion process along these variables. The idea is that the presence of auxiliary variables mixes external randomness that helps to corrupt sensitive input data earlier on in the diffusion process. This concept is theoretically investigated and validated on a toy dataset and a speech dataset using the Area Under the Receiver Operating Characteristic (AUROC) curves and the FID metric.

Elizabeth Fons, Alejandro Sztrajman, Yousef El-Laham et al.

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.

Yousef El-Laham, Niccolò Dalmasso, Svitlana Vyetrenko et al.

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.

Haibei Zhu, Yousef El-Laham, Elizabeth Fons et al.

Effective utilization of time series data is often constrained by the scarcity of data quantity that reflects complex dynamics, especially under the condition of distributional shifts. Existing datasets may not encompass the full range of statistical properties required for robust and comprehensive analysis. And privacy concerns can further limit their accessibility in domains such as finance and healthcare. This paper presents an approach that utilizes large language models and data source interfaces to explore and collect time series datasets. While obtained from external sources, the collected data share critical statistical properties with primary time series datasets, making it possible to model and adapt to various scenarios. This method enlarges the data quantity when the original data is limited or lacks essential properties. It suggests that collected datasets can effectively supplement existing datasets, especially involving changes in data distribution. We demonstrate the effectiveness of the collected datasets through practical examples and show how time series forecasting foundation models fine-tuned on these datasets achieve comparable performance to those models without fine-tuning.