Covariance Prediction via Convex Optimization
This work addresses covariance prediction for statistical modeling, but it appears incremental as it builds on existing generalized linear model frameworks without claiming major breakthroughs.
The paper tackles the problem of predicting the covariance of a zero-mean Gaussian vector using a feature vector, proposing a generalized linear model predictor that involves convex optimization for fitting. The result is a method that can be combined or recursively applied to enhance performance, though no concrete numbers are provided.
We consider the problem of predicting the covariance of a zero mean Gaussian vector, based on another feature vector. We describe a covariance predictor that has the form of a generalized linear model, i.e., an affine function of the features followed by an inverse link function that maps vectors to symmetric positive definite matrices. The log-likelihood is a concave function of the predictor parameters, so fitting the predictor involves convex optimization. Such predictors can be combined with others, or recursively applied to improve performance.