<commit_before>;; gorilla-repl.fileformat = 1

;; **
;;; # Gaussian
;; **

;; **
;;; Import the minimum required libraries to run define queries, compile them, and run the inference using compiled artifacts.
;; **

;; @@
(ns worksheets.gaussian
  (:require [anglican.runtime :refer :all]
            [anglican.emit :refer [defquery]]
            [anglican.stat :refer [empirical-distribution collect-results]]
            anglican.infcomp.csis
            anglican.importance
            [anglican.infcomp.network :refer :all]
            [anglican.inference :refer [infer]])
  (:use [gorilla-plot core]))
;; @@

;; **
;;; Define a Gaussian unknown mean model
;; **

;; @@
(defquery gaussian [obs]
  (let [mean (sample "mean" (normal 0 1))
        std 0.1]
    (observe (normal mean std) obs)
    mean))
;; @@

;; **
;;; ## Inference Compilation
;; **

;; **
;;; Specify a function `combine-observes-fn` that combines observes from a sample in a form suitable for Torch:
;; **

;; @@
(defn combine-observes-fn [observes]
  (:value (first observes)))
;; @@

;; **
;;; In order to write this function, you'll need to look at how a typical `observes` object from your query looks like:
;; **

;; @@
(sample-observes-from-prior gaussian [1])
;; @@

;; **
;;; Compile our query
;; **

;; @@
(def torch-connection (start-torch-connection gaussian [1] combine-observes-fn))
;; @@

;; **
;;; Then run the following to train the neural network:
;;;
;;; `python -m infcomp.compile`
;; **

;; @@
(stop-torch-connection torch-connection)
;; @@

;; **
;;; ## Inference
;; **

;; **
;;; First, run the inference server from torch-infcomp:
;;;
;;; `python -m infcomp.infer`
;;;
;;; Then run the query, specifying number of particles:
;; **

;; @@
(def num-particles 100)
(def csis-states (take num-particles (infer :csis gaussian [2.3])))
(list-plot (vec (empirical-distribution (collect-results csis-states))))
;; @@

;; **
;;; Using the same number of particles, we don't have such good results with importance sampling:
;; **

;; @@
(def num-particles 100)
(def is-states (take num-particles (infer :importance gaussian [2.3])))
(list-plot (vec (empirical-distribution (collect-results is-states))))
;; @@<commit_msg>gaussian worksheet without string addresses<commit_after>;; gorilla-repl.fileformat = 1

;; **
;;; # Gaussian
;; **

;; **
;;; Import the minimum required libraries to run define queries, compile them, and run the inference using compiled artifacts.
;; **

;; @@
(ns worksheets.gaussian
  (:require [anglican.runtime :refer :all]
            [anglican.emit :refer [defquery query]]
            [anglican.stat :refer [empirical-distribution collect-results]]
            anglican.infcomp.csis
            anglican.importance
            anglican.infcomp.core
            [anglican.infcomp.network :refer :all]
            [anglican.inference :refer [infer]])
  (:use [gorilla-plot core]))

(anglican.infcomp.core/reset-infcomp-addressing-scheme!)
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-unkown'>#function[anglican.infcomp.core/reset-infcomp-addressing-scheme!$fn--26656$fn--26657]</span>","value":"#function[anglican.infcomp.core/reset-infcomp-addressing-scheme!$fn--26656$fn--26657]"}
;; <=

;; **
;;; Define a Gaussian unknown mean model
;; **

;; @@
(defquery gaussian [obs]
  (let [mean (sample (normal 0 1))
        std 0.1]
    (observe (normal mean std) obs)
    mean))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;worksheets.gaussian/gaussian</span>","value":"#'worksheets.gaussian/gaussian"}
;; <=

;; **
;;; ## Inference Compilation
;; **

;; **
;;; Specify a function `combine-observes-fn` that combines observes from a sample in a form suitable for Torch:
;; **

;; @@
(defn combine-observes-fn [observes]
  (:value (first observes)))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;worksheets.gaussian/combine-observes-fn</span>","value":"#'worksheets.gaussian/combine-observes-fn"}
;; <=

;; **
;;; In order to write this function, you'll need to look at how a typical `observes` object from your query looks like:
;; **

;; @@
(sample-samples-from-prior gaussian [1])
;; @@
;; =>
;;; {"type":"list-like","open":"<span class='clj-vector'>[</span>","close":"<span class='clj-vector'>]</span>","separator":" ","items":[{"type":"list-like","open":"<span class='clj-map'>{</span>","close":"<span class='clj-map'>}</span>","separator":", ","items":[{"type":"list-like","open":"","close":"","separator":" ","items":[{"type":"html","content":"<span class='clj-keyword'>:time-index</span>","value":":time-index"},{"type":"html","content":"<span class='clj-unkown'>0</span>","value":"0"}],"value":"[:time-index 0]"},{"type":"list-like","open":"","close":"","separator":" ","items":[{"type":"html","content":"<span class='clj-keyword'>:sample-address</span>","value":":sample-address"},{"type":"html","content":"<span class='clj-string'>&quot;S6&quot;</span>","value":"\"S6\""}],"value":"[:sample-address \"S6\"]"},{"type":"list-like","open":"","close":"","separator":" ","items":[{"type":"html","content":"<span class='clj-keyword'>:sample-instance</span>","value":":sample-instance"},{"type":"html","content":"<span class='clj-unkown'>0</span>","value":"0"}],"value":"[:sample-instance 0]"},{"type":"list-like","open":"","close":"","separator":" ","items":[{"type":"html","content":"<span class='clj-keyword'>:distribution</span>","value":":distribution"},{"type":"html","content":"<span class='clj-unkown'>#object[anglican.infcomp.flatbuffers.normal.NormalClj 0x482db72c &quot;anglican.infcomp.flatbuffers.normal.NormalClj@482db72c&quot;]</span>","value":"#object[anglican.infcomp.flatbuffers.normal.NormalClj 0x482db72c \"anglican.infcomp.flatbuffers.normal.NormalClj@482db72c\"]"}],"value":"[:distribution #object[anglican.infcomp.flatbuffers.normal.NormalClj 0x482db72c \"anglican.infcomp.flatbuffers.normal.NormalClj@482db72c\"]]"},{"type":"list-like","open":"","close":"","separator":" ","items":[{"type":"html","content":"<span class='clj-keyword'>:value</span>","value":":value"},{"type":"html","content":"<span class='clj-double'>-0.8529945048633982</span>","value":"-0.8529945048633982"}],"value":"[:value -0.8529945048633982]"}],"value":"{:time-index 0, :sample-address \"S6\", :sample-instance 0, :distribution #object[anglican.infcomp.flatbuffers.normal.NormalClj 0x482db72c \"anglican.infcomp.flatbuffers.normal.NormalClj@482db72c\"], :value -0.8529945048633982}"}],"value":"[{:time-index 0, :sample-address \"S6\", :sample-instance 0, :distribution #object[anglican.infcomp.flatbuffers.normal.NormalClj 0x482db72c \"anglican.infcomp.flatbuffers.normal.NormalClj@482db72c\"], :value -0.8529945048633982}]"}
;; <=

;; **
;;; Compile our query
;; **

;; @@
(def torch-connection (start-torch-connection gaussian [1] combine-observes-fn))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;worksheets.gaussian/torch-connection</span>","value":"#'worksheets.gaussian/torch-connection"}
;; <=

;; **
;;; Then run the following to train the neural network:
;;; 
;;; `python -m infcomp.compile`
;; **

;; @@
(stop-torch-connection torch-connection)
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-string'>&quot;Torch connection terminated.&quot;</span>","value":"\"Torch connection terminated.\""}
;; <=

;; **
;;; ## Inference
;; **

;; **
;;; First, run the inference server from torch-infcomp:
;;; 
;;; `python -m infcomp.infer`
;;; 
;;; Then run the query, specifying number of particles:
;; **

;; @@
(defn posterior-mean-std [prior-mean prior-std observation-std test-observations]
  (let [prior-variance (* prior-std prior-std)
        observation-variance (* observation-std observation-std)
        num-observations (count test-observations)
        posterior-mean (+ (/ (* observation-variance prior-mean)
                              (+ (* num-observations prior-variance) observation-variance))
                           (/ (* num-observations prior-variance (/ (reduce + test-observations) num-observations))
                              (+ (* num-observations prior-variance) observation-variance)))
        posterior-variance (/ 1 (+ (/ 1 prior-variance) (/ num-observations observation-variance)))]
    [posterior-mean (Math/sqrt posterior-variance)]))

(def test-observations [2.3])
(def prior-mean 0)
(def prior-std 1)
(def observation-std 0.1)

(def posterior-dist (apply normal (posterior-mean-std prior-mean prior-std observation-std test-observations)))
(def posterior-plot (plot #(Math/exp (observe* posterior-dist %)) [-3 3]))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;worksheets.gaussian/posterior-plot</span>","value":"#'worksheets.gaussian/posterior-plot"}
;; <=

;; @@
(def num-particles 100)
(def csis-states (take num-particles (infer :csis gaussian test-observations)))
(compose
  posterior-plot
  (histogram (repeatedly 10000 #(sample* (categorical (vec (empirical-distribution (collect-results csis-states)))))) :normalize :probability-density))
;; @@
;; =>
;;; 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;; <=

;; **
;;; Using the same number of particles, we don't have such good results with importance sampling:
;; **

;; @@
(def num-particles 100)
(def is-states (take num-particles (infer :importance gaussian test-observations)))
(compose
  posterior-plot
  (histogram (repeatedly 10000 #(sample* (categorical (vec (empirical-distribution (collect-results is-states)))))) :normalize :probability-density))
;; @@
;; =>
;;; 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