Self-Supervised Learning for Covariance Estimation

We consider the use of deep learning for covariance estimation. We propose to globally learn a neural network that will then be applied locally at inference time. Leveraging recent advancements in self-supervised foundational models, we train the network without any labeling by simply masking different samples and learning to predict their covariance given their surrounding neighbors. The architecture is based on the popular attention mechanism. Its main advantage over classical methods is the automatic exploitation of global characteristics without any distributional assumptions or regularization. It can be pre-trained as a foundation model and then be repurposed for various downstream tasks, e.g., adaptive target detection in radar or hyperspectral imagery

Learning to Estimate Without Bias

The Gauss Markov theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non-linear settings via deep learning with bias constraints. The classical approach to designing non-linear MVUEs is through maximum likelihood estimation (MLE) which often involves real-time computationally challenging optimizations. On the other hand, deep learning methods allow for non-linear estimators with fixed computational complexity. Learning based estimators perform optimally on average with respect to their training set but may suffer from significant bias in other parameters. To avoid this, we propose to add a simple bias constraint to the loss function, resulting in an estimator we refer to as Bias Constrained Estimator (BCE). We prove that this yields asymptotic MVUEs that behave similarly to the classical MLEs and asymptotically attain the Cramer Rao bound. We demonstrate the advantages of our approach in the context of signal to noise ratio estimation as well as covariance estimation. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance. Examples include distributed sensor networks and data augmentation in test-time. In such applications, we show that BCE leads to asymptotically consistent estimators

CFARnet: deep learning for target detection with constant false alarm rate

We consider the problem of learning detectors with a Constant False Alarm Rate (CFAR). Classical model-based solutions to composite hypothesis testing are sensitive to imperfect models and are often computationally expensive. In contrast, data-driven machine learning is often more robust and yields classifiers with fixed computational complexity. Learned detectors usually do not have a CFAR as required in many applications. To close this gap, we introduce CFARnet where the loss function is penalized to promote similar distributions of the detector under any null hypothesis scenario. Asymptotic analysis in the case of linear models with general Gaussian noise reveals that the classical generalized likelihood ratio test (GLRT) is actually a minimizer of the CFAR constrained Bayes risk. Experiments in both synthetic data and real hyper-spectral images show that CFARnet leads to near CFAR detectors with similar accuracy as their competitors.Comment: arXiv admin note: substantial text overlap with arXiv:2206.0574

Probabilistic Simplex Component Analysis by Importance Sampling

In this paper we consider the problem of linear unmixing hidden random variables defined over the simplex with additive Gaussian noise, also known as probabilistic simplex component analysis (PRISM). Previous solutions to tackle this challenging problem were based on geometrical approaches or computationally intensive variational methods. In contrast, we propose a conventional expectation maximization (EM) algorithm which embeds importance sampling. For this purpose, the proposal distribution is chosen as a simple surrogate distribution of the target posterior that is guaranteed to lie in the simplex. This distribution is based on the Gaussian linear minimum mean squared error (LMMSE) approximation which is accurate at high signal-to-noise ratio. Numerical experiments in different settings demonstrate the advantages of this adaptive surrogate over state-of-the-art methods

Deep robust regression

International audienc