Ledoit-Wolf linear shrinkage with unknown mean

This work addresses large dimensional covariance matrix estimation with unknown mean. The empirical covariance estimator fails when dimension and number of samples are proportional and tend to infinity, settings known as Kolmogorov asymptotics. When the mean is known, Ledoit and Wolf (2004) proposed a linear shrinkage estimator and proved its convergence under those asymptotics. To the best of our knowledge, no formal proof has been proposed when the mean is unknown. To address this issue, we propose a new estimator and prove its quadratic convergence under the Ledoit and Wolf assumptions. Finally, we show empirically that it outperforms other standard estimators.

On some theoretical limitations of Generative Adversarial Networks

Generative Adversarial Networks have become a core technique in Machine Learning to generate unknown distributions from data samples. They have been used in a wide range of context without paying much attention to the possible theoretical limitations of those models. Indeed, because of the universal approximation properties of Neural Networks, it is a general assumption that GANs can generate any probability distribution. Recently, people began to question this assumption and this article is in line with this thinking. We provide a new result based on Extreme Value Theory showing that GANs can't generate heavy tailed distributions. The full proof of this result is given.

Adversarial trading

Adversarial samples have drawn a lot of attention from the Machine Learning community in the past few years. An adverse sample is an artificial data point coming from an imperceptible modification of a sample point aiming at misleading. Surprisingly, in financial research, little has been done in relation to this topic from a concrete trading point of view. We show that those adversarial samples can be implemented in a trading environment and have a negative impact on certain market participants. This could have far reaching implications for financial markets either from a trading or a regulatory point of view.

An empirical study of neural networks for trend detection in time series

Detecting structure in noisy time series is a difficult task. One intuitive feature is the notion of trend. From theoretical hints and using simulated time series, we empirically investigate the efficiency of standard recurrent neural networks (RNNs) to detect trends. We show the overall superiority and versatility of certain standard RNNs structures over various other estimators. These RNNs could be used as basic blocks to build more complex time series trend estimators.