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Quantitative Finance · Glosarium

Apa itu Quantile regression, mixture density network?

Dikenal juga sebagai: quantile regression · mixture density network

Definition 11.4 Machine Learning for Markets · Bab 11 — Probabilistic Models and Uncertainty

Quantile regression fits the conditional α\alpha-quantile by minimising the average pinball loss Ln=1n∑iℓα(yi,fθ(xi))\mathcal L_n = \frac1n\sum_i\ell_\alpha(y_i, f_\theta(x_i)) (Koenker and Bassett, 1978); with several levels it describes the whole distribution. A mixture density network outputs the weights, means and standard deviations of a mixture of KK Gaussians and is trained by their negative log-likelihood (Bishop, 1994).

before day 2 100after day 2 100
modelCRPS (bp)90% coverageCRPS (bp)90% coverage
boosted quantiles78.989.4%136.385.0%
Gaussian network (one seed)79.090.6%135.387.0%
ensemble of five79.191.1%135.487.6%
mixture density network78.889.7%136.186.1%
truth (Gaussian approximation)78.991.2%135.591.3%
Table 11.1. Distributional forecasts of the next day’s return on the test days of twenty synthetic assets. CRPS computed on nineteen quantiles (5% to 95%), in basis points of return. Data: ml_uncert.scores.
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