fastmath.gp
Gaussian Processes
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Categories
Other vars: ->GaussianProcess L gaussian-process posterior-samples predict predict-all prior-samples
gaussian-process
(gaussian-process xss ys)(gaussian-process xss ys {:keys [kscale kernel noise normalize? L?], :or {kscale 1.0, kernel (k/kernel :gaussian 1.0), normalize? false, noise 1.0E-8, L? true}})Examples
Object creation
(gaussian-process [1 2 3] [-1 2 1])
;;=> fastmath.gp.GaussianProcess@7860dc0e
(gaussian-process [1 2 3]
[-1 2 1]
{:normalize? true,
:kernel (k/kernel :gaussian 0.5),
:kscale 2.0,
:noise 0.1})
;;=> fastmath.gp.GaussianProcess@4cee1580posterior-samples
(posterior-samples gp-object xvals)(posterior-samples gp-object xvals stddev?)Examples
With gaussian kernel
(let [gp (gaussian-process [-5 1 2]
[17 10 12]
{:kernel (k/kernel :gaussian 0.5)})]
(posterior-samples gp (range -5 2 0.9)))
;;=> (16.999884359640117
;;=> 3.1208039260060736
;;=> 0.0765520018114407
;;=> -0.5522472618655202
;;=> -0.33565663425825365
;;=> 1.6468976690043093
;;=> 4.983383079352442
;;=> 10.567358405881329)Plot of 10 posteriors (with gaussian kernel)
With periodic kernel
(let [gp (gaussian-process [-5 1 2]
[17 10 12]
{:kernel (k/kernel :periodic 0.2 6.5)})]
(posterior-samples gp (range -5 2 0.9)))
;;=> (17.000057569911778
;;=> 1.8683865502451709
;;=> 0.4018489935338301
;;=> 0.12330897258784282
;;=> 0.1178539023717543
;;=> 0.5093262455624785
;;=> -0.33890970733205694
;;=> 13.305376406992414)Plot of 10 posteriors (with periodic kernel)
predict
(predict gp-object xval)(predict gp-object xval stddev?)Examples
Usage
(let [gp (gaussian-process [-5 1 2] [17 10 12])]
[(gp 1.1) (predict gp 1.1)])
;;=> [10.546027301365227 10.546027301365227]Predict and return standard deviation
(let [gp (gaussian-process [-5 1 2] [17 10 12])]
[(gp 1.1 true) (predict gp 1.1 true)])
;;=> [[10.546027301365227 0.05980825454330318]
;;=> [10.546027301365227 0.05980825454330318]]Gaussian process with confidence intervals
Predict and return standard deviation for normalized process
(let [gp (gaussian-process [-5 1 2] [17 10 12] {:normalize? true})]
[(gp 1.1 true) (predict gp 1.1 true)])
;;=> [[10.09725781658689 0.2156417284518817]
;;=> [10.09725781658689 0.2156417284518817]]Gaussian process with confidence intervals for normalized process
predict-all
(predict-all gp-object xvals)(predict-all gp-object xvals stddev?)Examples
Usage
(let [gp (gaussian-process [-5 1 2] [17 10 12])]
(predict-all gp [-5 -2 1 2 3]))
;;=> (16.999999829999997
;;=> 0.23983287597866382
;;=> 9.99999995694442
;;=> 11.999999906114532
;;=> 6.277135459489308)Predict and return standard deviation
(let [gp (gaussian-process [-5 1 2] [17 10 12])]
(predict-all gp [-5 -2 1 2 3] true))
;;=> ([16.999999829999997 9.999999969612645E-5]
;;=> [0.23983287597866382 0.9998441540162327]
;;=> [9.99999995694442 9.999999858590342E-5]
;;=> [11.999999906114532 9.99999980307919E-5]
;;=> [6.277135459489308 0.739305317305734])prior-samples
(prior-samples gp-object xvals)Examples
Usage
(let [gp (gaussian-process [0 1 -2 -2.001] [-2 3 0.5 -0.6])]
(prior-samples gp (range 0 1 0.1)))
;;=> (-0.792983868612105
;;=> -0.6778147362568855
;;=> -0.5444855711770306
;;=> -0.39524525991973797
;;=> -0.2333700621293956
;;=> -0.06280864555710398
;;=> 0.1122325565000701
;;=> 0.28770104917887485
;;=> 0.46004918213031654
;;=> 0.6264783531606577
;;=> 0.7850508460072277)Plot of 10 priors
With added noise
(let [gp
(gaussian-process [0 1 -2 -2.001] [-2 3 0.5 -0.6] {:noise 0.1})]
(prior-samples gp (range 0 1 0.1)))
;;=> (1.618775231635548
;;=> 1.6996793940243753
;;=> 1.7789859925516815
;;=> 1.8530283478463896
;;=> 1.9184179959440781
;;=> 1.9723383193987132
;;=> 2.0127647549733356
;;=> 2.0385803980887585
;;=> 2.0495734736475284
;;=> 2.046323665069238
;;=> 2.0300035786626176)Plot of 10 priors (with noise)
