From 76a0f254ea16c9b519c29ca96fda1c0a562555b4 Mon Sep 17 00:00:00 2001 From: Quinn Dougherty Date: Wed, 20 Apr 2022 11:55:56 -0400 Subject: [PATCH 1/7] removed pull request trigger from codeql analysis --- .github/workflows/codeql-analysis.yml | 7 - .parcelrc | 6 - packages/website/docs/Features/Functions.mdx | 169 +++++++++++++++---- packages/website/docs/Internal/Invariants.md | 20 ++- 4 files changed, 158 insertions(+), 44 deletions(-) delete mode 100644 .parcelrc diff --git a/.github/workflows/codeql-analysis.yml b/.github/workflows/codeql-analysis.yml index c7750177..2aef3ae3 100644 --- a/.github/workflows/codeql-analysis.yml +++ b/.github/workflows/codeql-analysis.yml @@ -18,13 +18,6 @@ on: - production - staging - develop - pull_request: - # The branches below must be a subset of the branches above - branches: - - master - - production - - staging - - develop schedule: - cron: "42 19 * * 0" diff --git a/.parcelrc b/.parcelrc deleted file mode 100644 index f5a5c2d5..00000000 --- a/.parcelrc +++ /dev/null @@ -1,6 +0,0 @@ -{ - "extends": "@parcel/config-default", - "transformers": { - "*.res": ["@parcel/transformer-raw"] - } -} diff --git a/packages/website/docs/Features/Functions.mdx b/packages/website/docs/Features/Functions.mdx index 7e0d1fc6..5e09004c 100644 --- a/packages/website/docs/Features/Functions.mdx +++ b/packages/website/docs/Features/Functions.mdx @@ -1,69 +1,101 @@ --- +title: Functions reference sidebar_position: 7 --- import { SquiggleEditor } from "../../src/components/SquiggleEditor"; -# Squiggle Functions Reference +_The source of truth for this document is [this file of code](https://github.com/quantified-uncertainty/squiggle/blob/develop/packages/squiggle-lang/src/rescript/ReducerInterface/ReducerInterface_GenericDistribution.res)_ -## Distributions +# Inventory distributions -### Normal distribution +We provide starter distributions, computed symbolically. + +## Normal distribution The `normal(mean, sd)` function creates a normal distribution with the given mean and standard deviation. -### Uniform distribution +### Validity +- `sd > 0` + +## Uniform distribution The `uniform(low, high)` function creates a uniform distribution between the two given numbers. -### Lognormal distribution +### Validity +- `low < high` + +## Lognormal distribution The `lognormal(mu, sigma)` returns the log of a normal distribution with parameters -mu and sigma. The log of lognormal(mu, sigma) is a normal distribution with parameters -mean mu and standard deviation sigma. +`mu` and `sigma`. The log of `lognormal(mu, sigma)` is a normal distribution with mean `mu` and standard deviation `sigma`. -An alternative format is also available. The "to" notation creates a lognormal +An alternative format is also available. The `to` notation creates a lognormal distribution with a 90% confidence interval between the two numbers. We add this convinience as lognormal distributions are commonly used in practice. +### Future feature: Furthermore, it's also possible to create a lognormal from it's actual mean and standard deviation, using `lognormalFromMeanAndStdDev`. -### Beta distribution +### Validity +- `sigma > 0` +- In `x to y` notation, `x < y` -The `beta(a, b)` function creates a beta distribution with parameters a and b: +## Beta distribution + +The `beta(a, b)` function creates a beta distribution with parameters `a` and `b`: -### Exponential distribution +### Validity +- `a > 0` +- `b > 0` +- Empirically, we have noticed that numerical instability arises when `a < 1` or `b < 1` -The `exponential(mean)` function creates an exponential distribution with the given -mean. +## Exponential distribution + +The `exponential(rate)` function creates an exponential distribution with the given +rate. -### The Triangular distribution +### Validity +- `rate > 0` + +## Triangular distribution The `triangular(a,b,c)` function creates a triangular distribution with lower -bound a, mode b and upper bound c. +bound `a`, mode `b` and upper bound `c`. + +### Validity +- `a < b < c` -### Multimodal distriutions +## Scalar (constant dist) -The multimodal function combines 2 or more other distributions to create a weighted +Squiggle, when the context is right, automatically casts a float to a constant distribution. + +# Operating on distributions + +Here are the ways we combine distributions. + +## Mixture of distributions + +The `mx` function combines 2 or more other distributions to create a weighted combination of the two. The first positional arguments represent the distributions to be combined, and the last argument is how much to weigh every distribution in the combination. @@ -78,37 +110,114 @@ As well as mixed distributions: -## Other Functions +An alias of `mx` is `mixture` -### PDF of a distribution +### Validity +Using javascript's variable arguments notation, consider `mx(...dists, weights)`: +- `dists.length == weights.length` -The `pdf(distribution, x)` function returns the density of a distribution at the +## Addition (horizontal right shift) + + + +## Subtraction (horizontal left shift) + + + +## Multiplication (??) + + + +## Division (???) + + + +## Taking the base `e` exponential + + + +## Taking the base `e` and base `10` logarithm + + + + + +### Validity +- See [the current discourse](https://github.com/quantified-uncertainty/squiggle/issues/304) + +# Standard functions on distributions + +## Probability density function + +The `pdf(dist, x)` function returns the density of a distribution at the given point x. -### Inverse of a distribution +### Validity +- `x` must be a scalar +- `dist` must be a distribution -The `inv(distribution, prob)` gives the value x or which the probability for all values -lower than x is equal to prob. It is the inverse of `cdf`. +## Cumulative density function - - -### CDF of a distribution - -The `cdf(distribution,x)` gives the cumulative probability of the distribution +The `cdf(dist, x)` gives the cumulative probability of the distribution or all values lower than x. It is the inverse of `inv`. -### Mean of a distribution +### Validity +- `x` must be a scalar +- `dist` must be a distribution + +## Inverse CDF + +The `inv(dist, prob)` gives the value x or which the probability for all values +lower than x is equal to prob. It is the inverse of `cdf`. + + + +### Validity +- `prob` must be a scalar (please only put it in `(0,1)`) +- `dist` must be a distribution + +## Mean The `mean(distribution)` function gives the mean (expected value) of a distribution. -### Sampling a distribution +## Sampling a distribution The `sample(distribution)` samples a given distribution. + +# Normalization + +Some distribution operations (like horizontal shift) return an unnormalized distriibution. + +We provide a `normalize` function + + +### Valdity +- Input to `normalize` must be a dist + +We provide a predicate `isNormalized`, for when we have simple control flow + + + +### Validity +- Input to `isNormalized` must be a dist + +# Convert any distribution to a sample set distribution + +`toSampleSet` has two signatures + +It is unary when you use an internal hardcoded number of samples + + + +And binary when you provide a number of samples (truncated) + + + diff --git a/packages/website/docs/Internal/Invariants.md b/packages/website/docs/Internal/Invariants.md index c1c0fd79..633c904b 100644 --- a/packages/website/docs/Internal/Invariants.md +++ b/packages/website/docs/Internal/Invariants.md @@ -1,5 +1,5 @@ --- -title: Statistical properties of algebraic combinations of distributions for property testing. +title: Invariants urlcolor: blue author: - Nuño Sempere @@ -7,8 +7,12 @@ author: abstract: This document outlines some properties about algebraic combinations of distributions. It is meant to facilitate property tests for [Squiggle](https://squiggle-language.com/), an estimation language for forecasters. So far, we are focusing on the means, the standard deviation and the shape of the pdfs. --- +Invariants to check with property tests. + _This document right now is normative and aspirational, not a description of the testing that's currently done_. +# Algebraic combinations + The academic keyword to search for in relation to this document is "[algebra of random variables](https://wikiless.org/wiki/Algebra_of_random_variables?lang=en)". Squiggle doesn't yet support getting the standard deviation, denoted by $\sigma$, but such support could yet be added. ## Means and standard deviations @@ -118,6 +122,20 @@ TODO TODO +# `pdf`, `cdf`, and `inv` + +With $\forall dist, pdf := x \mapsto \texttt{pdf}(dist, x) \land cdf := x \mapsto \texttt{cdf}(dist, x) \land inv := p \mapsto \texttt{inv}(dist, p)$, + +## `cdf` and `inv` are inverses +$$ +\forall x \in (0,1), cdf(inv(x)) = x \land \forall x \in \texttt{dom}(cdf), x = inv(cdf(x)) +$$ + +## The codomain of `cdf` equals the open interval `(0,1)` equals the codomain of `pdf` +$$ +\texttt{cod}(cdf) = (0,1) = \texttt{cod}(pdf) +$$ + # To do: - Provide sources or derivations, useful as this document becomes more complicated From 9cdffc309beeecc4fa3b516200d3a71581c1617b Mon Sep 17 00:00:00 2001 From: Quinn Dougherty Date: Wed, 20 Apr 2022 12:09:57 -0400 Subject: [PATCH 2/7] functions reference is almost done --- packages/website/.prettierignore | 2 + packages/website/docs/Features/Functions.mdx | 62 +++++++++++++++----- packages/website/docs/Internal/Invariants.md | 8 ++- 3 files changed, 55 insertions(+), 17 deletions(-) create mode 100644 packages/website/.prettierignore diff --git a/packages/website/.prettierignore b/packages/website/.prettierignore new file mode 100644 index 00000000..d858cd65 --- /dev/null +++ b/packages/website/.prettierignore @@ -0,0 +1,2 @@ +.docusaurus +build diff --git a/packages/website/docs/Features/Functions.mdx b/packages/website/docs/Features/Functions.mdx index 5e09004c..5cba7c11 100644 --- a/packages/website/docs/Features/Functions.mdx +++ b/packages/website/docs/Features/Functions.mdx @@ -9,7 +9,7 @@ _The source of truth for this document is [this file of code](https://github.com # Inventory distributions -We provide starter distributions, computed symbolically. +We provide starter distributions, computed symbolically. ## Normal distribution @@ -19,6 +19,7 @@ and standard deviation. ### Validity + - `sd > 0` ## Uniform distribution @@ -29,6 +30,7 @@ two given numbers. ### Validity + - `low < high` ## Lognormal distribution @@ -44,13 +46,15 @@ this convinience as lognormal distributions are commonly used in practice. -### Future feature: +### Future feature: + Furthermore, it's also possible to create a lognormal from it's actual mean and standard deviation, using `lognormalFromMeanAndStdDev`. ### Validity + - `sigma > 0` - In `x to y` notation, `x < y` @@ -61,6 +65,7 @@ The `beta(a, b)` function creates a beta distribution with parameters `a` and `b ### Validity + - `a > 0` - `b > 0` - Empirically, we have noticed that numerical instability arises when `a < 1` or `b < 1` @@ -73,6 +78,7 @@ rate. ### Validity + - `rate > 0` ## Triangular distribution @@ -81,17 +87,18 @@ The `triangular(a,b,c)` function creates a triangular distribution with lower bound `a`, mode `b` and upper bound `c`. ### Validity + - `a < b < c` ## Scalar (constant dist) -Squiggle, when the context is right, automatically casts a float to a constant distribution. +Squiggle, when the context is right, automatically casts a float to a constant distribution. # Operating on distributions -Here are the ways we combine distributions. +Here are the ways we combine distributions. ## Mixture of distributions @@ -110,10 +117,12 @@ As well as mixed distributions: -An alias of `mx` is `mixture` +An alias of `mx` is `mixture` ### Validity -Using javascript's variable arguments notation, consider `mx(...dists, weights)`: + +Using javascript's variable arguments notation, consider `mx(...dists, weights)`: + - `dists.length == weights.length` ## Addition (horizontal right shift) @@ -124,7 +133,7 @@ Using javascript's variable arguments notation, consider `mx(...dists, weights)` -## Multiplication (??) +## Multiplication (??) @@ -136,16 +145,17 @@ Using javascript's variable arguments notation, consider `mx(...dists, weights)` -## Taking the base `e` and base `10` logarithm +## Taking the base `e` and base `10` logarithm ### Validity + - See [the current discourse](https://github.com/quantified-uncertainty/squiggle/issues/304) -# Standard functions on distributions +# Standard functions on distributions ## Probability density function @@ -155,6 +165,7 @@ given point x. ### Validity + - `x` must be a scalar - `dist` must be a distribution @@ -166,6 +177,7 @@ or all values lower than x. It is the inverse of `inv`. ### Validity + - `x` must be a scalar - `dist` must be a distribution @@ -177,6 +189,7 @@ lower than x is equal to prob. It is the inverse of `cdf`. ### Validity + - `prob` must be a scalar (please only put it in `(0,1)`) - `dist` must be a distribution @@ -194,19 +207,19 @@ The `sample(distribution)` samples a given distribution. # Normalization -Some distribution operations (like horizontal shift) return an unnormalized distriibution. +Some distribution operations (like horizontal shift) return an unnormalized distriibution. We provide a `normalize` function -### Valdity -- Input to `normalize` must be a dist +### Valdity - Input to `normalize` must be a dist -We provide a predicate `isNormalized`, for when we have simple control flow +We provide a predicate `isNormalized`, for when we have simple control flow -### Validity +### Validity + - Input to `isNormalized` must be a dist # Convert any distribution to a sample set distribution @@ -221,3 +234,24 @@ And binary when you provide a number of samples (truncated) +# `inspect` + +You may like to debug by right clicking your browser and using the _inspect_ functionality on the webpage, and viewing the _console_ tab. Then, wrap your squiggle output with `inspect` to log an internal representation. + + + +Save for a logging side effect, `inspect` does nothing to input and returns it. + +# Truncate + +You can cut off from the left + + + +You can cut off from the right + + + +You can cut off from both sides + + diff --git a/packages/website/docs/Internal/Invariants.md b/packages/website/docs/Internal/Invariants.md index 633c904b..85fd56be 100644 --- a/packages/website/docs/Internal/Invariants.md +++ b/packages/website/docs/Internal/Invariants.md @@ -7,7 +7,7 @@ author: abstract: This document outlines some properties about algebraic combinations of distributions. It is meant to facilitate property tests for [Squiggle](https://squiggle-language.com/), an estimation language for forecasters. So far, we are focusing on the means, the standard deviation and the shape of the pdfs. --- -Invariants to check with property tests. +Invariants to check with property tests. _This document right now is normative and aspirational, not a description of the testing that's currently done_. @@ -122,16 +122,18 @@ TODO TODO -# `pdf`, `cdf`, and `inv` +# `pdf`, `cdf`, and `inv` -With $\forall dist, pdf := x \mapsto \texttt{pdf}(dist, x) \land cdf := x \mapsto \texttt{cdf}(dist, x) \land inv := p \mapsto \texttt{inv}(dist, p)$, +With $\forall dist, pdf := x \mapsto \texttt{pdf}(dist, x) \land cdf := x \mapsto \texttt{cdf}(dist, x) \land inv := p \mapsto \texttt{inv}(dist, p)$, ## `cdf` and `inv` are inverses + $$ \forall x \in (0,1), cdf(inv(x)) = x \land \forall x \in \texttt{dom}(cdf), x = inv(cdf(x)) $$ ## The codomain of `cdf` equals the open interval `(0,1)` equals the codomain of `pdf` + $$ \texttt{cod}(cdf) = (0,1) = \texttt{cod}(pdf) $$ From b9ad87fda7555d81efa9b387ac37a39110d38f90 Mon Sep 17 00:00:00 2001 From: Quinn Dougherty Date: Wed, 20 Apr 2022 12:15:07 -0400 Subject: [PATCH 3/7] squiggle syntax in `initialSquiggleString` for `trunctate` --- packages/website/docs/Features/Functions.mdx | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/packages/website/docs/Features/Functions.mdx b/packages/website/docs/Features/Functions.mdx index 5cba7c11..2dacd2fe 100644 --- a/packages/website/docs/Features/Functions.mdx +++ b/packages/website/docs/Features/Functions.mdx @@ -254,4 +254,4 @@ You can cut off from the right You can cut off from both sides - + From 15ccf876a64af389d5930afe4793abbf2ed64f75 Mon Sep 17 00:00:00 2001 From: Quinn Dougherty Date: Wed, 20 Apr 2022 12:26:03 -0400 Subject: [PATCH 4/7] fixed `/>` bug --- packages/website/docs/Features/Functions.mdx | 22 ++++++++++---------- 1 file changed, 11 insertions(+), 11 deletions(-) diff --git a/packages/website/docs/Features/Functions.mdx b/packages/website/docs/Features/Functions.mdx index 2dacd2fe..f4fd3aab 100644 --- a/packages/website/docs/Features/Functions.mdx +++ b/packages/website/docs/Features/Functions.mdx @@ -1,5 +1,5 @@ --- -title: Functions reference +title: "Functions reference" sidebar_position: 7 --- @@ -62,7 +62,7 @@ and standard deviation, using `lognormalFromMeanAndStdDev`. The `beta(a, b)` function creates a beta distribution with parameters `a` and `b`: - + ### Validity @@ -75,7 +75,7 @@ The `beta(a, b)` function creates a beta distribution with parameters `a` and `b The `exponential(rate)` function creates an exponential distribution with the given rate. - + ### Validity @@ -127,29 +127,29 @@ Using javascript's variable arguments notation, consider `mx(...dists, weights)` ## Addition (horizontal right shift) - + ## Subtraction (horizontal left shift) - + ## Multiplication (??) - + ## Division (???) - + ## Taking the base `e` exponential - + ## Taking the base `e` and base `10` logarithm - + - + ### Validity @@ -230,7 +230,7 @@ It is unary when you use an internal hardcoded number of samples -And binary when you provide a number of samples (truncated) +And binary when you provide a number of samples (floored) From 9f35039b60d8dda949f0247f240865083f26ee71 Mon Sep 17 00:00:00 2001 From: Quinn Dougherty Date: Wed, 20 Apr 2022 13:41:22 -0400 Subject: [PATCH 5/7] second pass; one CR comment --- packages/website/docs/Features/Functions.mdx | 136 ++++++++++++------- packages/website/docs/Internal/Invariants.md | 28 ++-- 2 files changed, 104 insertions(+), 60 deletions(-) diff --git a/packages/website/docs/Features/Functions.mdx b/packages/website/docs/Features/Functions.mdx index f4fd3aab..cfc308ee 100644 --- a/packages/website/docs/Features/Functions.mdx +++ b/packages/website/docs/Features/Functions.mdx @@ -1,5 +1,5 @@ --- -title: "Functions reference" +title: "Functions Reference" sidebar_position: 7 --- @@ -7,33 +7,33 @@ import { SquiggleEditor } from "../../src/components/SquiggleEditor"; _The source of truth for this document is [this file of code](https://github.com/quantified-uncertainty/squiggle/blob/develop/packages/squiggle-lang/src/rescript/ReducerInterface/ReducerInterface_GenericDistribution.res)_ -# Inventory distributions +## Inventory distributions We provide starter distributions, computed symbolically. -## Normal distribution +### Normal distribution The `normal(mean, sd)` function creates a normal distribution with the given mean and standard deviation. -### Validity +#### Validity - `sd > 0` -## Uniform distribution +### Uniform distribution The `uniform(low, high)` function creates a uniform distribution between the two given numbers. -### Validity +#### Validity - `low < high` -## Lognormal distribution +### Lognormal distribution The `lognormal(mu, sigma)` returns the log of a normal distribution with parameters `mu` and `sigma`. The log of `lognormal(mu, sigma)` is a normal distribution with mean `mu` and standard deviation `sigma`. @@ -46,183 +46,227 @@ this convinience as lognormal distributions are commonly used in practice. -### Future feature: +#### Future feature: Furthermore, it's also possible to create a lognormal from it's actual mean and standard deviation, using `lognormalFromMeanAndStdDev`. -### Validity +#### Validity - `sigma > 0` - In `x to y` notation, `x < y` -## Beta distribution +### Beta distribution The `beta(a, b)` function creates a beta distribution with parameters `a` and `b`: -### Validity +#### Validity - `a > 0` - `b > 0` - Empirically, we have noticed that numerical instability arises when `a < 1` or `b < 1` -## Exponential distribution +### Exponential distribution The `exponential(rate)` function creates an exponential distribution with the given rate. -### Validity +#### Validity - `rate > 0` -## Triangular distribution +### Triangular distribution The `triangular(a,b,c)` function creates a triangular distribution with lower bound `a`, mode `b` and upper bound `c`. -### Validity +#### Validity - `a < b < c` -## Scalar (constant dist) +### Scalar (constant dist) Squiggle, when the context is right, automatically casts a float to a constant distribution. -# Operating on distributions +## Operating on distributions Here are the ways we combine distributions. -## Mixture of distributions +### Mixture of distributions -The `mx` function combines 2 or more other distributions to create a weighted +The `mixture` function combines 2 or more other distributions to create a weighted combination of the two. The first positional arguments represent the distributions to be combined, and the last argument is how much to weigh every distribution in the combination. - + It's possible to create discrete distributions using this method. - + As well as mixed distributions: - + -An alias of `mx` is `mixture` +An alias of `mixture` is `mx` -### Validity +#### Validity Using javascript's variable arguments notation, consider `mx(...dists, weights)`: - `dists.length == weights.length` -## Addition (horizontal right shift) +### Addition (horizontal right shift) -## Subtraction (horizontal left shift) +### Subtraction (horizontal left shift) -## Multiplication (??) +### Multiplication (??) -## Division (???) +We also provide concatenation of two distributions as a syntax sugar for `*` + + + +### Division (???) -## Taking the base `e` exponential +### Exponentiation (???) + + + +### Taking the base `e` exponential -## Taking the base `e` and base `10` logarithm +### Taking logarithms -### Validity +Base `x` + +#### Validity + +- `x` must be a scalar - See [the current discourse](https://github.com/quantified-uncertainty/squiggle/issues/304) -# Standard functions on distributions +### Pointwise addition -## Probability density function +**Pointwise operations are done with `PointSetDist` internals rather than `SampleSetDist` internals**. + +TODO: this isn't in the new interpreter/parser yet. + + + +### Pointwise subtraction + +TODO: this isn't in the new interpreter/parser yet. + + + +### Pointwise multiplication + + + +### Pointwise division + + + +### Pointwise exponentiation + + + +### Pointwise logarithm + +TODO: write about the semantics and the case handling re scalar vs. dist and log base. + + + +## Standard functions on distributions + +### Probability density function The `pdf(dist, x)` function returns the density of a distribution at the given point x. -### Validity +#### Validity - `x` must be a scalar - `dist` must be a distribution -## Cumulative density function +### Cumulative density function The `cdf(dist, x)` gives the cumulative probability of the distribution or all values lower than x. It is the inverse of `inv`. -### Validity +#### Validity - `x` must be a scalar - `dist` must be a distribution -## Inverse CDF +### Inverse CDF The `inv(dist, prob)` gives the value x or which the probability for all values lower than x is equal to prob. It is the inverse of `cdf`. -### Validity +#### Validity - `prob` must be a scalar (please only put it in `(0,1)`) - `dist` must be a distribution -## Mean +### Mean The `mean(distribution)` function gives the mean (expected value) of a distribution. -## Sampling a distribution +### Sampling a distribution The `sample(distribution)` samples a given distribution. -# Normalization +## Normalization Some distribution operations (like horizontal shift) return an unnormalized distriibution. We provide a `normalize` function -### Valdity - Input to `normalize` must be a dist +#### Validity - Input to `normalize` must be a dist We provide a predicate `isNormalized`, for when we have simple control flow -### Validity +#### Validity - Input to `isNormalized` must be a dist -# Convert any distribution to a sample set distribution +## Convert any distribution to a sample set distribution `toSampleSet` has two signatures @@ -234,7 +278,7 @@ And binary when you provide a number of samples (floored) -# `inspect` +## `inspect` You may like to debug by right clicking your browser and using the _inspect_ functionality on the webpage, and viewing the _console_ tab. Then, wrap your squiggle output with `inspect` to log an internal representation. @@ -242,7 +286,7 @@ You may like to debug by right clicking your browser and using the _inspect_ fun Save for a logging side effect, `inspect` does nothing to input and returns it. -# Truncate +## Truncate You can cut off from the left diff --git a/packages/website/docs/Internal/Invariants.md b/packages/website/docs/Internal/Invariants.md index 85fd56be..8a89466a 100644 --- a/packages/website/docs/Internal/Invariants.md +++ b/packages/website/docs/Internal/Invariants.md @@ -11,13 +11,13 @@ Invariants to check with property tests. _This document right now is normative and aspirational, not a description of the testing that's currently done_. -# Algebraic combinations +## Algebraic combinations The academic keyword to search for in relation to this document is "[algebra of random variables](https://wikiless.org/wiki/Algebra_of_random_variables?lang=en)". Squiggle doesn't yet support getting the standard deviation, denoted by $\sigma$, but such support could yet be added. -## Means and standard deviations +### Means and standard deviations -### Sums +#### Sums $$ mean(f+g) = mean(f) + mean(g) @@ -33,7 +33,7 @@ $$ mean(normal(a,b) + normal(c,d)) = mean(normal(a+c, \sqrt{b^2 + d^2})) $$ -### Subtractions +#### Subtractions $$ mean(f-g) = mean(f) - mean(g) @@ -43,7 +43,7 @@ $$ \sigma(f-g) = \sqrt{\sigma(f)^2 + \sigma(g)^2} $$ -### Multiplications +#### Multiplications $$ mean(f \cdot g) = mean(f) \cdot mean(g) @@ -53,15 +53,15 @@ $$ \sigma(f \cdot g) = \sqrt{ (\sigma(f)^2 + mean(f)) \cdot (\sigma(g)^2 + mean(g)) - (mean(f) \cdot mean(g))^2} $$ -### Divisions +#### Divisions Divisions are tricky, and in general we don't have good expressions to characterize properties of ratios. In particular, the ratio of two normals is a Cauchy distribution, which doesn't have to have a mean. -## Probability density functions (pdfs) +### Probability density functions (pdfs) Specifying the pdf of the sum/multiplication/... of distributions as a function of the pdfs of the individual arguments can still be done. But it requires integration. My sense is that this is still doable, and I (Nuño) provide some _pseudocode_ to do this. -### Sums +#### Sums Let $f, g$ be two independently distributed functions. Then, the pdf of their sum, evaluated at a point $z$, expressed as $(f + g)(z)$, is given by: @@ -114,31 +114,31 @@ let pdfOfSum = (pdf1, pdf2, cdf1, cdf2, z) => { }; ``` -## Cumulative density functions +### Cumulative density functions TODO -## Inverse cumulative density functions +### Inverse cumulative density functions TODO -# `pdf`, `cdf`, and `inv` +## `pdf`, `cdf`, and `inv` With $\forall dist, pdf := x \mapsto \texttt{pdf}(dist, x) \land cdf := x \mapsto \texttt{cdf}(dist, x) \land inv := p \mapsto \texttt{inv}(dist, p)$, -## `cdf` and `inv` are inverses +### `cdf` and `inv` are inverses $$ \forall x \in (0,1), cdf(inv(x)) = x \land \forall x \in \texttt{dom}(cdf), x = inv(cdf(x)) $$ -## The codomain of `cdf` equals the open interval `(0,1)` equals the codomain of `pdf` +### The codomain of `cdf` equals the open interval `(0,1)` equals the codomain of `pdf` $$ \texttt{cod}(cdf) = (0,1) = \texttt{cod}(pdf) $$ -# To do: +## To do: - Provide sources or derivations, useful as this document becomes more complicated - Provide definitions for the probability density function, exponential, inverse, log, etc. From 8b83c9ec844f8a14435b3c076e6dd9fbd5bab533 Mon Sep 17 00:00:00 2001 From: Quinn Dougherty Date: Wed, 20 Apr 2022 14:55:14 -0400 Subject: [PATCH 6/7] CR pass thru; cleanup; no more scientific notation --- packages/website/docs/Features/Functions.mdx | 52 +++++++++++++------- packages/website/docs/Internal/Invariants.md | 2 +- 2 files changed, 34 insertions(+), 20 deletions(-) diff --git a/packages/website/docs/Features/Functions.mdx b/packages/website/docs/Features/Functions.mdx index cfc308ee..e1564fc6 100644 --- a/packages/website/docs/Features/Functions.mdx +++ b/packages/website/docs/Features/Functions.mdx @@ -42,7 +42,7 @@ The `lognormal(mu, sigma)` returns the log of a normal distribution with paramet An alternative format is also available. The `to` notation creates a lognormal distribution with a 90% confidence interval between the two numbers. We add -this convinience as lognormal distributions are commonly used in practice. +this convenience as lognormal distributions are commonly used in practice. @@ -51,6 +51,8 @@ this convinience as lognormal distributions are commonly used in practice. Furthermore, it's also possible to create a lognormal from it's actual mean and standard deviation, using `lognormalFromMeanAndStdDev`. +TODO: interpreter/parser doesn't provide this in current `develop` branch + #### Validity @@ -62,7 +64,7 @@ and standard deviation, using `lognormalFromMeanAndStdDev`. The `beta(a, b)` function creates a beta distribution with parameters `a` and `b`: - + #### Validity @@ -75,7 +77,7 @@ The `beta(a, b)` function creates a beta distribution with parameters `a` and `b The `exponential(rate)` function creates an exponential distribution with the given rate. - + #### Validity @@ -125,29 +127,39 @@ Using javascript's variable arguments notation, consider `mx(...dists, weights)` - `dists.length == weights.length` -### Addition (horizontal right shift) +### Addition + +A horizontal right shift -### Subtraction (horizontal left shift) +### Subtraction + +A horizontal left shift -### Multiplication (??) +### Multiplication + +TODO: provide intuition pump for the semantics We also provide concatenation of two distributions as a syntax sugar for `*` - + -### Division (???) +### Division + +TODO: provide intuition pump for the semantics -### Exponentiation (???) +### Exponentiation - +TODO: provide intuition pump for the semantics + + ### Taking the base `e` exponential @@ -161,7 +173,8 @@ We also provide concatenation of two distributions as a syntax sugar for `*` Base `x` - + + #### Validity - `x` must be a scalar @@ -255,12 +268,13 @@ Some distribution operations (like horizontal shift) return an unnormalized dist We provide a `normalize` function - + + #### Validity - Input to `normalize` must be a dist We provide a predicate `isNormalized`, for when we have simple control flow - + #### Validity @@ -272,17 +286,17 @@ We provide a predicate `isNormalized`, for when we have simple control flow It is unary when you use an internal hardcoded number of samples - + And binary when you provide a number of samples (floored) - + ## `inspect` You may like to debug by right clicking your browser and using the _inspect_ functionality on the webpage, and viewing the _console_ tab. Then, wrap your squiggle output with `inspect` to log an internal representation. - + Save for a logging side effect, `inspect` does nothing to input and returns it. @@ -290,12 +304,12 @@ Save for a logging side effect, `inspect` does nothing to input and returns it. You can cut off from the left - + You can cut off from the right - + You can cut off from both sides - + diff --git a/packages/website/docs/Internal/Invariants.md b/packages/website/docs/Internal/Invariants.md index 8a89466a..91adf1a1 100644 --- a/packages/website/docs/Internal/Invariants.md +++ b/packages/website/docs/Internal/Invariants.md @@ -1,5 +1,5 @@ --- -title: Invariants +title: Invariants of Probability Distributions urlcolor: blue author: - Nuño Sempere From be6beac944ec10913d3d91acb63447c0fa320124 Mon Sep 17 00:00:00 2001 From: Quinn Dougherty Date: Wed, 20 Apr 2022 16:50:43 -0400 Subject: [PATCH 7/7] multiline `initialSquiggleString`s; favicon! --- packages/website/docs/Features/Functions.mdx | 83 +++++++++++++++---- packages/website/docusaurus.config.js | 10 +-- packages/website/src/pages/index.js | 5 +- packages/website/static/img/favicon.ico | Bin 3626 -> 6611 bytes packages/website/static/img/quri-logo.png | Bin 0 -> 20214 bytes 5 files changed, 74 insertions(+), 24 deletions(-) create mode 100644 packages/website/static/img/quri-logo.png diff --git a/packages/website/docs/Features/Functions.mdx b/packages/website/docs/Features/Functions.mdx index e1564fc6..c85a3438 100644 --- a/packages/website/docs/Features/Functions.mdx +++ b/packages/website/docs/Features/Functions.mdx @@ -131,19 +131,31 @@ Using javascript's variable arguments notation, consider `mx(...dists, weights)` A horizontal right shift - + ### Subtraction A horizontal left shift - + ### Multiplication TODO: provide intuition pump for the semantics - + We also provide concatenation of two distributions as a syntax sugar for `*` @@ -153,27 +165,44 @@ We also provide concatenation of two distributions as a syntax sugar for `*` TODO: provide intuition pump for the semantics - + ### Exponentiation TODO: provide intuition pump for the semantics - + ### Taking the base `e` exponential - + ### Taking logarithms - + - + Base `x` - + #### Validity @@ -186,31 +215,55 @@ Base `x` TODO: this isn't in the new interpreter/parser yet. - + ### Pointwise subtraction TODO: this isn't in the new interpreter/parser yet. - + ### Pointwise multiplication - + ### Pointwise division - + ### Pointwise exponentiation - + ### Pointwise logarithm TODO: write about the semantics and the case handling re scalar vs. dist and log base. - + ## Standard functions on distributions diff --git a/packages/website/docusaurus.config.js b/packages/website/docusaurus.config.js index c5d03327..4971b1b0 100644 --- a/packages/website/docusaurus.config.js +++ b/packages/website/docusaurus.config.js @@ -49,7 +49,7 @@ const config = { sidebarPath: require.resolve("./sidebars.js"), // Please change this to your repo. editUrl: - "https://github.com/quantified-uncertainty/squiggle/tree/master/packages/website/", + "https://github.com/quantified-uncertainty/squiggle/tree/develop/packages/website/", remarkPlugins: [math], rehypePlugins: [katex], }, @@ -57,7 +57,7 @@ const config = { showReadingTime: true, // Please change this to your repo. editUrl: - "https://github.com/quantified-uncertainty/squiggle/tree/master/packages/website/", + "https://github.com/quantified-uncertainty/squiggle/tree/develop/packages/website/", }, theme: { customCss: require.resolve("./src/css/custom.css"), @@ -73,7 +73,7 @@ const config = { title: "Squiggle", logo: { alt: "Squiggle Logo", - src: "img/logo.svg", + src: "img/quri-logo.png", }, items: [ { @@ -85,7 +85,7 @@ const config = { { to: "/blog", label: "Blog", position: "left" }, { to: "/playground", label: "Playground", position: "left" }, { - href: "https://github.com/QURIresearch/squiggle", + href: "https://github.com/quantified-uncertainty/squiggle", label: "GitHub", position: "right", }, @@ -103,7 +103,7 @@ const config = { }, { label: "GitHub", - href: "https://github.com/QURIresearch/squiggle", + href: "https://github.com/quantified-uncertainty/squiggle", }, ], }, diff --git a/packages/website/src/pages/index.js b/packages/website/src/pages/index.js index 452c7ef0..4cbddcac 100644 --- a/packages/website/src/pages/index.js +++ b/packages/website/src/pages/index.js @@ -22,10 +22,7 @@ function HomepageHeader() { export default function Home() { const { siteConfig } = useDocusaurusContext(); return ( - +
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