4-Computing-on-distributed-matrices.Rpres

Computing on distributed matrices
========================================================
author: Andrie de Vries & Michele Usuelli
date: 2015-07-01, UseR!2015
width: 1680
height: 1050
css: css/custom.css


Linear regression
=============

$$Y = X \beta + e$$

To solve for `b`, create a loss function, differentiate and solve for a minimum:

$$B = (X’X)^{-1} X’Y$$

Re-arrange:

$$(X’X) \beta = X’ Y$$

The R function  `b <- solve(x, y)` gives the solution to  $xb = y$

```{r, eval=FALSE}
b <- solve(x’x, x’y)
```

The math of distributed computing
=================================

* Commutative property

$$a + b  == b + a$$

* Associative property

$$(a + b) + c == a + (b + c)$$

* Distributive property

$$a * (b + c) == (a * b) + (b * c)$$



Computing X'X is a distributive operation
=============

![](images/SSCP-matrix.png)

Regression
==========

```{r taxi-2-rmr-local, cache=FALSE, include=FALSE}
read_chunk("demo/09-linear-regression.R")
```

```{r load-packages}
```

Regression
==========

```{r generate-data}
```

Regression
==========

```{r sum-function}
```

Regression
==========

```{r XtX}
```

Regression
==========

```{r XtY}
```

Regression
==========

```{r solve}
```