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Detecting early signs of depressive and manic episodes in patients with bipolar disorder using the signature-based model
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Recurrent major mood episodes and subsyndromal mood instability cause substantial disability in patients with bipolar disorder. Early identification of mood episodes enabling timely mood stabilisation is an important clinical goal. Recent technological advances allow the prospective reporting of mood in real time enabling more accurate, efficient data capture. The complex nature of these data streams in combination with challenge of deriving meaning from missing data mean pose a significant analytic challenge. The signature method is derived from stochastic analysis and has the ability to capture important properties of complex ordered time series data. To explore whether the onset of episodes of mania and depression can be identified using self-reported mood data.
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Regularized Learning for Fractional Brownian Motion via Path Signatures
The paper derives some moment bounds for signatures of fractional Brownian motion and shows simulations where signature Lasso beats Lasso, but it never proves the claimed consistency.
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