update itl docs

afsl/acquisition_functions/itl.py

@@ -36,9 +36,9 @@ class ITL(TargetedBaCE):
 
     #### Computation
 
-    `ITL` is computed using \\[\begin{align}
-        \I{\vf(\spA)}{y(\vx) \mid \spD_i} &= \frac{1}{2} \log\left( \frac{k_i(\vx,\vx) + \sigma^2}{\tilde{k}_i(\vx,\vx) + \sigma^2} \right) \qquad\text{where} \\\\
-        \tilde{k}_i(\vx,\vx) &= k_i(\vx,\vx) - \vk_i(\vx,\spA) \mK_i(\spA,\spA)^{-1} \vk_i(\spA,\vx)
+    `ITL` is computed using $\I{\vf(\spA)}{y(\vx) \mid \spD_i} \approx \I{\vy(\spA)}{y(\vx) \mid \spD_i}$ with \\[\begin{align}
+        \I{\vy(\spA)}{y(\vx) \mid \spD_i} &= \frac{1}{2} \log\left( \frac{k_i(\vx,\vx) + \sigma^2}{\tilde{k}_i(\vx,\vx) + \sigma^2} \right) \qquad\text{where} \\\\
+        \tilde{k}_i(\vx,\vx) &= k_i(\vx,\vx) - \vk_i(\vx,\spA) (\mK_i(\spA,\spA) + \sigma^2 \mI)^{-1} \vk_i(\spA,\vx)
     \end{align}\\] where $\sigma^2$ is the noise variance and $k_i$ denotes the conditional kernel (see afsl.acquisition_functions.bace.BaCE).
 
     [^1]: A kernel $k$ on domain $\spX$ induces a stochastic process $\\{f(\vx)\\}_{\vx \in \spX}$. See afsl.model.ModelWithKernel.