Hugo Inzirillo

Hugo Inzirillo, Ludovic De Villelongue

Deep learning is playing an increasingly important role in time series analysis. We focused on time series forecasting using attention free mechanism, a more efficient framework, and proposed a new architecture for time series prediction for which linear models seem to be unable to capture the time dependence. We proposed an architecture built using attention free LSTM layers that overcome linear models for conditional variance prediction. Our findings confirm the validity of our model, which also allowed to improve the prediction capacity of a LSTM, while improving the efficiency of the learning task.

Hugo Inzirillo, Ludovic De Villelongue

It is difficult to identify anomalies in time series, especially when there is a lot of noise. Denoising techniques can remove the noise but this technique can cause a significant loss of information. To detect anomalies in the time series we have proposed an attention free conditional autoencoder (AF-CA). We started from the autoencoder conditional model on which we added an Attention-Free LSTM layer \cite{inzirillo2022attention} in order to make the anomaly detection capacity more reliable and to increase the power of anomaly detection. We compared the results of our Attention Free Conditional Autoencoder with those of an LSTM Autoencoder and clearly improved the explanatory power of the model and therefore the detection of anomaly in noisy time series.

Rémi Genet, Hugo Inzirillo

In this paper, we propose a novel approach that enhances recurrent neural networks (RNNs) by incorporating path signatures into their gating mechanisms. Our method modifies both Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) architectures by replacing their forget and reset gates, respectively, with learnable path signatures. These signatures, which capture the geometric features of the entire path history, provide a richer context for controlling information flow through the network's memory. This modification allows the networks to make memory decisions based on the full historical context rather than just the current input and state. Through experimental studies, we demonstrate that our Signature-LSTM (SigLSTM) and Signature-GRU (SigGRU) models outperform their traditional counterparts across various sequential learning tasks. By leveraging path signatures in recurrent architectures, this method offers new opportunities to enhance performance in time series analysis and forecasting applications.

Rémi Genet, Hugo Inzirillo

In this paper we introduce Keras Sig a high-performance pythonic library designed to compute path signature for deep learning applications. Entirely built in Keras 3, \textit{Keras Sig} leverages the seamless integration with the mostly used deep learning backends such as PyTorch, JAX and TensorFlow. Inspired by Kidger and Lyons (2021),we proposed a novel approach reshaping signature calculations to leverage GPU parallelism. This adjustment allows us to reduce the training time by 55\% and 5 to 10-fold improvements in direct signature computation compared to existing methods, while maintaining similar CPU performance. Relying on high-level tensor operations instead of low-level C++ code, Keras Sig significantly reduces the versioning and compatibility issues commonly encountered in deep learning libraries, while delivering superior or comparable performance across various hardware configurations. We demonstrate through extensive benchmarking that our approach scales efficiently with the length of input sequences and maintains competitive performance across various signature parameters, though bounded by memory constraints for very large signature dimensions.

Hugo Inzirillo

We propose a new way of building portfolios of cryptocurrencies that provide good diversification properties to investors. First, we seek to filter these digital assets by creating some clusters based on their path signature. The goal is to identify similar patterns in the behavior of these highly volatile assets. Once such clusters have been built, we propose "optimal" portfolios by comparing the performances of such portfolios to a universe of unfiltered digital assets. Our intuition is that clustering based on path signatures will make it easier to capture the main trends and features of a group of cryptocurrencies, and allow parsimonious portfolios that reduce excessive transaction fees. Empirically, our assumptions seem to be satisfied.

Hugo Inzirillo, Remi Genet

Traditional Smooth Transition Autoregressive (STAR) models offer an effective way to model these dynamics through smooth regime changes based on specific transition variables. In this paper, we propose a novel approach by drawing an analogy between STAR models and a multilayer neural network architecture. Our proposed neural network architecture mimics the STAR framework, employing multiple layers to simulate the smooth transition between regimes and capturing complex, nonlinear relationships. The network's hidden layers and activation functions are structured to replicate the gradual switching behavior typical of STAR models, allowing for a more flexible and scalable approach to regime-dependent modeling. This research suggests that neural networks can provide a powerful alternative to STAR models, with the potential to enhance predictive accuracy in economic and financial forecasting.

Hugo Schnoering, Hugo Inzirillo

The study of time series has motivated many researchers, particularly on the area of multivariate-analysis. The study of co-movements and dependency between random variables leads us to develop metrics to describe existing connection between assets. The most commonly used are correlation and causality. Despite the growing literature, some connections remained still undetected. The objective of this paper is to propose a new representation learning algorithm capable to integrate synchronous and asynchronous relationships.

Hugo Inzirillo, Benjamin Mat

The objective of this paper is to assess the performances of dimensionality reduction techniques to establish a link between cryptocurrencies. We have focused our analysis on the two most traded cryptocurrencies: Bitcoin and Ethereum. To perform our analysis, we took log returns and added some covariates to build our data set. We first introduced the pearson correlation coefficient in order to have a preliminary assessment of the link between Bitcoin and Ethereum. We then reduced the dimension of our data set using canonical correlation analysis and principal component analysis. After performing an analysis of the links between Bitcoin and Ethereum with both statistical techniques, we measured their performance on forecasting Ethereum returns with Bitcoin s features.