Random sampling

Random sampling in PyTorch is implemented by the functions here and in the section on parameter initialization.

bernoulli

torch.bernoulli is implemented by function bernoulli().

Draws binary random numbers (0 or 1) from a Bernoulli distribution.

The input should contain probabilities to be used for drawing the binary random number, with all values in the range: \(0 \leq \text{x}_i \leq 1\).

The \(\text{i}^{th}\) element of the output will draw a value \(1\) according to the \(\text{i}^{th}\) probability value given in the input.

\[\text{out}_{i} \sim \mathrm{Bernoulli}(p = \text{x}_{i}) \]

bernoulli(x) → Bernoulli values

bernoulli(x;output) → null

Parameters:

• x (array,tensor) – a k array or tensor of floating point numbers between 0 and 1 indicating the probability of drawing a 1

• output (tensor) – an optional output tensor, may be of integral type

Returns:

Returns an array if k array input, else tensor, of same shape as the input x with 0`s and 1`s drawn according to the porbaility in the input. If output tensor supplied, output is written to the tensor and null is returned.

q)seed 0
q)bernoulli 5 3# .1 .5 .99e
0 0 1
0 1 1
0 0 1
0 1 1
1 1 1

q)r:tensor 0#0b
q)bernoulli(5 3# .1 .5 .99e;r)
q)tensor r
001b
011b
011b
001b
111b

q)seed 0
q)x:tensor 1 2 3 4%4
q)y:bernoulli x
q)tensor y
0 0 1 1f

multinomial

torch.multinomial is implemented by multinomial(), which returns an array or tensor where each row contains indices sampled from the multinomial probability distribution located in the corresponding row of the input.

multinomial(x;n;replace) → indices

multinomial(x;n;replace;output) → null

Allowable argument combinations:

• multinomial(x)

• multinomial(x;n)

• multinomial(x;n;replace)

• multinomial(x;replace)

• any of the above combinations followed by a trailing output tensor

Param:

array,tensor x: a 1-dim or 2-dim array or tensor with probabilities or weights

Param:

long n: optional, set to 1 if not specified, the number of samples (per row if 2-dim input)

Param:

bool replace: flag set false by default, set true to allow samples to be drawn with replacement

Param:

tensor output: an optional output tensor

Returns:

Returns an list or array if input is a k list or array, else a tensor of indices sampled. If an output tensor supplied, the indices are written to the supplied tensor and null returned.

q)seed 123

q)multinomial .2 .6 .4
1

q)multinomial(.2 .6 .4;10;1b)
0 1 1 1 1 2 0 2 0 1

q)x:(.2 .6 .4; .5 .0 .5)

q)multinomial x
1 2

q)multinomial(x;4;1b)
1 1 1 2
0 2 0 2