IntegralVarianceReduction¶
- class probnum.quad.solvers.acquisition_functions.IntegralVarianceReduction¶
Bases:
AcquisitionFunction
The normalized reduction of the integral variance.
The acquisition function is
\[\begin{split}a(x) &= \mathfrak{v}^{-1}(\mathfrak{v} - \mathfrak{v}(x))\\ &= \frac{(\int \bar{k}(x', x)p(x')\mathrm{d}x')^2}{\mathfrak{v} v(x)}\\ &= \rho^2(x)\end{split}\]where \(\mathfrak{v}\) is the current integral variance, \(\mathfrak{v}(x)\) is the integral variance including a hypothetical observation at \(x\), \(v(x)\) is the predictive variance for \(f(x)\) and \(\bar{k}(x', x)\) is the posterior kernel function.
The value \(a(x)\) is equal to the squared correlation \(\rho^2(x)\) between the hypothetical observation at \(x\) and the integral value. [1]
The normalization constant \(\mathfrak{v}^{-1}\) ensures that \(a(x)\in[0, 1]\).
References
Attributes Summary
Whether the acquisition function exposes gradients.
Methods Summary
__call__
(x, bq_state)Evaluates the acquisition function and optionally its gradients.
Attributes Documentation
- has_gradients¶
Methods Documentation
- __call__(x, bq_state)[source]¶
Evaluates the acquisition function and optionally its gradients.
- Parameters:
- Returns:
acquisition_values – shape=(batch_size, ) – The acquisition values at nodes
x
.acquisition_gradients – shape=(batch_size, input_dim) – The corresponding gradients (optional).
- Return type: