Changes between Initial Version and Version 1 of BysVecLinReg

Timestamp:

May 6, 2010, 4:05:51 PM (15 years ago)

Author:

Víctor de Buen Remiro

Comment:

--

BysVecLinReg

@@ +1 @@
+= BysVecLinReg =
+
+BysVecLinReg yields for Bayesian simulator of Vectorial Linear Regression with arbitrary constraining inequations
+
+Vectorial linear regression equations are [[BR]]
+
+[[LatexEquation(Y=A \cdot X + E)]] [[BR]]
+
+where [[BR]]
+
+ * [[LatexEquation(Y\in\mathbb{R}^{d\times N} )]] is the multivariant known output matrix, where each row is a different output vector [[LatexEquation(y_{n}\in\mathbb{R}^{N} )]]  [[BR]]
+ * [[LatexEquation(X\in\mathbb{R}^{m\times N} )]] is the known and full rank input matrix, where each row is a different input vector [[LatexEquation(x_{n}\in\mathbb{R}^{N} )]] [[BR]]
+ * [[LatexEquation(A\in\mathbb{R}^{d\times m} )]] has the unknown regression coefficients that we want to estimate [[BR]]
+ * [[LatexEquation(E\in\mathbb{R}^{d\times N} )]] is the multivariant residuals, where each row is the residuals vector  [[LatexEquation(e_{n}\in\mathbb{R}^{N} )]] corresponding to output [[LatexEquation(y_{n} )]] 
+ 
+All residuals inside the same row are incorrelated normal, but resiudals in the same column [[LatexEquation(j)]] are [[BR]] 
+
+[[LatexEquation(e_{.,j} \sim N\left(0,V\right) E\in\mathbb{R}^{d\times d} \forall j=1 \ldots d )]][[BR]]
+
+where [[LatexEquation(V)]] is symmetric positive definite and unknown, but the same for each column[[BR]]
+
+When there are some restriction over parameters inside [[LatexEquation(A)]] we must to add the inequations of feasible region [[BR]]
+
+[[LatexEquation(\Omega = \left\{ A\in\mathbb{R}^{d\times m} \mid F\left(A\right) \le 0 \right\})]] [[BR]] 
+
+being [[BR]]
+
+[[LatexEquation( F\left(A\right):\mathbb{R}^{d\times m}\longrightarrow\mathbb{R}^{r} )]]  [[BR]]
+
+the constraining function. [[BR]]
+
+The method used in this package is based on [http://research.microsoft.com/en-us/um/people/minka/papers/minka-linear.ps.gz  Bayesian linear regression Thomas Minka (2001)]