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VALENCE

Est. 2007 · Berkeley, California

Signal extraction where the noise dominates.

Statistical Machine Learning in Low Signal-to-Noise Regimes. We develop state-space estimators, shrinkage methods and reproducible research infrastructure for non-stationary, high-dimensional data.

Research programme

Three problems, one discipline.

Non-stationary state estimation

State-space models and adaptive filters for latent quantities that drift, switch regimes, and are observed only through heavy measurement noise.

High-dimensional estimation

Shrinkage, regularization and random-matrix theory for covariance and regression problems where the number of variables is comparable to the sample size.

Compute-efficient inference

Deterministic, auditable research pipelines: seeded computation, content-addressed artifacts and benchmarks that can be reproduced by anyone.

Methodology

Optimal weighting, made explicit.

In a scalar random-walk model with process variance qq and observation variance rr, the steady-state Kalman gain depends only on the signal-to-noise ratio. When r≫qr \gg q, the gain scales with the square root of the ratio, which fixes the effective averaging window of the estimator.

K∞=P∞P∞+r,P∞=q+q2+4qr2K_\infty = \frac{P_\infty}{P_\infty + r}, \qquad P_\infty = \frac{q + \sqrt{q^{2} + 4qr}}{2} K∞≈qras r≫qK_\infty \approx \sqrt{\frac{q}{r}} \qquad \text{as } r \gg q

Steady-state gain of the scalar Kalman filter for a random-walk latent level.

Research & engineering blog

Recent publications

All articles

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