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Attempt to define the VarInfo interface (#36)
* Add draft for varinfo interface description * Add some stuff * Update varinfo-interface.md Co-authored-by: Hong Ge <[email protected]> * Elaborate on model trace proposal * Update abstractmodeltrace-interface.md Co-authored-by: Hong Ge <[email protected]>
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# `AbstractModelTrace`/`VarInfo` interface proposal | ||
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## Background | ||
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### Why do we do this? | ||
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As I have said before: | ||
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> There are many aspects that make VarInfo a very complex data structure. | ||
Currently, there is an insane amount of complexity and implementation details in `varinfo.jl`, which | ||
has been rewritten multiple times with different concerns in mind – most times to improve concrete | ||
needs of Turing.jl, such as type stability, or requirements of specific samplers. | ||
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This unfortunately makes `VarInfo` extremely opaque: it is hard to refactor without breaking | ||
anything (nobody really dares touching it), and a lot of knowledge about Turing.jl/DynamicPPL.jl | ||
internals is needed in order to judge the effects of changes. | ||
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### Design choices | ||
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Recently, @torfjelde [has shown](https://github.com/TuringLang/DynamicPPL.jl/pull/267/files) that a | ||
much simpler implementation is feasible – basically, just a wrapped `NamedTuple` with a minimal | ||
interface. | ||
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The purpose of this proposal is twofold: first, to think about what a sufficient interface for | ||
`AbstractModelTrace`, the abstract supertype of `VarInfo`, should be, to allow multiple specialized | ||
variants and refactor the existing ones (typed/untyped and simple). Second, to view the problem as | ||
the design of an abstract data type: the specification of construction and modification mechanisms | ||
for a dictionary-like structure. | ||
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Related previous discussions: | ||
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- [Discussion about `VarName`](https://github.com/TuringLang/AbstractPPL.jl/discussions/7) | ||
- [`AbstractVarInfo` representation](https://github.com/TuringLang/AbstractPPL.jl/discussions/5) | ||
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Additionally (but closely related), the second part tries to formalize the “subsumption” mechanism | ||
of `VarName`s, and its interaction with using `VarName`s as keys/indices. | ||
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Our discussions take place in what is a bit of a fuzzy zone between the part that is really | ||
“abstract”, and meant for the wider purpuse of AbstractPPL.jl – the implementation of probabilistic | ||
programming systems in general – and our concrete needs within DPPL. I hope to always stay abstract | ||
and reusable; and there are already a couple of candidates for APPL clients other than DPPL, which | ||
will hopefully keep us focused: simulation based calibration, SimplePPL (a BUGS-like frontend), and | ||
ParetoSmoothing.jl. | ||
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### What is going to change? | ||
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- For the end user of Turing.jl: nothing. You usually don’t use `VarInfo`, or the raw evaluator | ||
interface, anyways. (Although if the newer data structures are more user-friendly, they might occur | ||
in more places in the future?) | ||
- For people having a look into code using `VarInfo`, or starting to hack on Turing.jl/DPPL.jl: a | ||
huge reduction in cognitive complexity. `VarInfo` implementations should be readable on their own, | ||
and the implemented functions layed out somewhere. Its usages should look like for any other nice, | ||
normal data structure. | ||
- For core DPPL.jl implementors: same as the previous, plus: a standard against which to improve and | ||
test `VarInfo`, and a clearly defined design space for new data structures. | ||
- For AbstractPPL.jl clients/PPL implementors: an interface to program against (as with the rest of | ||
APPL), and an existing set of well-specified, flexible trace data types with different | ||
characteristics. | ||
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And in terms of implementation work in DPPL.jl: once the interface is fixed (or even during fixing | ||
it), varinfo.jl will undergo a heavy refactoring – which should make it _simpler_! (No three | ||
different getter functions with slightly different semantics, etc…). | ||
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## Dictionary interface | ||
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The basic idea is for all `VarInfo`s to behave like ordered dictionaries with `VarName` keys – all | ||
common operations should just work. There are two things that make them more special, though: | ||
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1. “Fancy indexing”: since `VarName`s are structured themselves, the `VarInfo` should be have a bit | ||
like a trie, in the sense that all prefixes of stored keys should be retrievable. Also, | ||
subsumption of `VarName`s should be respected (see end of this document): | ||
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```julia | ||
vi[@varname(x.a)] = [1,2,3] | ||
vi[@varname(x.b)] = [4,5,6] | ||
vi[@varname(x.a[2])] == 2 | ||
vi[@varname(x)] == (; a = [1,2,3], b = [4,5,6]) | ||
``` | ||
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Generalizations that go beyond simple cases (those that you can imagine by storing individual | ||
`setfield!`s in a tree) need not be implemented in the beginning; e.g., | ||
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```julia | ||
vi[@varname(x[1])] = 1 | ||
vi[@varname(x[2])] = 2 | ||
keys(vi) == [x[1], x[2]] | ||
vi[@varname(x)] = [1,2] | ||
keys(vi) == [x] | ||
``` | ||
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2. (_This has to be discussed further._) Information other than the sampled values, such as flags, | ||
metadata, pointwise likelihoods, etc., can in principle be stored in multiple of these “`VarInfo` | ||
dicts” with parallel structure. For efficiency, it is thinkable to devise a design such that | ||
multiple fields can be stored under the same indexing structure. | ||
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```julia | ||
vi[@varname(x[1])] == 1 | ||
vi[@varname(x[1])].meta["bla"] == false | ||
``` | ||
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or something in that direction. | ||
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(This is logically equivalent to a dictionary with named tuple values. Maybe we can do what | ||
[`DictTable`](https://github.com/JuliaData/TypedTables.jl/blob/main/src/DictTable.jl) does?) | ||
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The old `order` field, indicating at which position in the evaluator function a variable has | ||
been added (essentially a counter of insertions) can actually be left out completely, since the | ||
dictionary is specified to be ordered by insertion. | ||
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The important question here is: should the “joint data structure” behave like a dictionary of | ||
`NamedTuple`s (`eltype(vi) == @NamedTuple{value::T, ℓ::Float64, meta}`), or like a struct of | ||
dicts with shared keys (`eltype(vi.value) <: T`, `eltype(vi.ℓ) <: Float64`, …)? | ||
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The required dictionary functions are about the following: | ||
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- Pure functions: | ||
- `iterate`, yielding pairs of `VarName` and the stored value | ||
- `IteratorEltype == HasEltype()`, `IteratorSize = HasLength()` | ||
- `keys`, `values`, `pairs`, `length` consistent with `iterate` | ||
- `eltype`, `keytype`, `valuetype` | ||
- `get`, `getindex`, `haskey` for indexing by `VarName` | ||
- `merge` to join two `VarInfo`s | ||
- Mutating functions: | ||
- `insert!!`, `set!!` | ||
- `merge!!` to add and join elements (TODO: think about `merge`) | ||
- `setindex!!` | ||
- `empty!!`, `delete!!`, `unset!!` (_Are these really used anywhere? Not having them makes persistent | ||
implementations much easier!_) | ||
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I believe that adopting the interface of | ||
[Dictionaries.jl](https://github.com/andyferris/Dictionaries.jl), not `Base.AbstractDict`, would be | ||
ideal, since their approach make key sharing and certain operations naturally easy (particularly | ||
“broadcast-style”, i.e., transformations on the values, but not the keys). | ||
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Other `Base` functions, like `enumerate`, should follow from the above. | ||
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`length` might appear weird – but it should definitely be consistent with the iterator. | ||
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It would be really cool if `merge` supported the combination of distinct types of implementations, | ||
e.g., a dynamic and a tuple-based part. | ||
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To support both mutable and immutable/persistent implementations, let’s require consistent | ||
BangBang.jl style mutators throughout. | ||
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## Transformations/Bijectors | ||
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Transformations should ideally be handled explicitely and from outside: automatically by the | ||
compiler macro, or at the places required by samplers. | ||
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Implementation-wise, they can probably be expressed as folds? | ||
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```julia | ||
map(v -> link(v.dist, v.value), vi) | ||
``` | ||
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## Linearization | ||
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There are multiple possible approaches to handle this: | ||
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1. As a special case of conversion: `Vector(vi)` | ||
2. `copy!(vals_array, vi)`. | ||
3. As a fold: `mapreduce(v -> vec(v.value), append!, vi, init=Float64[])` | ||
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Also here, I think that the best implementation would be through a fold. Variants (1) or (2) might | ||
additionally be provided as syntactic sugar. | ||
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--- | ||
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# `VarName`-based axioms | ||
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What follows is mostly an attempt to formalize subsumption. | ||
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First, remember that in Turing.jl we can always work with _concretized_ `VarName`s: `begin`/`end`, | ||
`:`, and boolean indexing are all turned into some form of concrete cartesian or array indexing | ||
(assuming [this suggestion](https://github.com/TuringLang/AbstractPPL.jl/issues/35) being | ||
implemented). This makes all index comparisons static. | ||
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Now, `VarName`s have a compositional structure: they can be built by composing a root variable with | ||
more and more lenses (`VarName{v}()` starts off with an `IdentityLens`): | ||
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```julia | ||
julia> vn = VarName{:x}() ∘ Setfield.IndexLens((1:10, 1) ∘ Setfield.IndexLens((2, ))) | ||
x[1:10,1][2] | ||
``` | ||
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(_Note that the composition function, `∘`, is really in wrong order; but this is a heritage of | ||
Setfield.jl._) | ||
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By “subsumption”, we mean the notion of a `VarName` expressing a more nested path than another one: | ||
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```julia | ||
subsumes(@varname(x.a), @varname(x.a[1])) | ||
@varname(x.a) ⊒ @varname(x.a[1]) # \sqsupseteq | ||
@varname(x.a) ⋢ @varname(x.a[1]) # \nsqsubseteq | ||
``` | ||
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Thus, we have the following axioms for `VarName`s (“variables” are `VarName{n}()`): | ||
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1. `x ⊑ x` for all variables `x` | ||
2. `x ≍ y` for `x ≠ y` (i.e., distinct variables are incomparable; `x ⋢ y` and `y ⋢ x`) (`≍` is `\asymp`) | ||
3. `x ∘ ℓ ⊑ x` for all variables `x` and lenses `ℓ` | ||
4. `x ∘ ℓ₁ ⊑ x ∘ ℓ₂ ⇔ ℓ₁ ⊑ ℓ₂` | ||
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For the last axiom to work, we also have to define subsumption of individual, non-composed lenses: | ||
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1. `PropertyLens(a) == PropertyLens(b) ⇔ a == b`, for all symbols `a`, `b` | ||
2. `FunctionLens(f) == FunctionLens(g) ⇔ f == g` (under extensional equality; I’m only mentioning | ||
this in case we ever generalize to Bijector-ed variables like `@varname(log(x))`) | ||
3. `IndexLens(ι₁) ⊑ IndexLens(ι₂)` if the index tuple `ι₂` covers all indices in `ι₁`; for example, | ||
`_[1, 2:10] ⊑ _[1:10, 1:20]`. (_This is a bit fuzzy and not all corner cases have been | ||
considered yet!_) | ||
4. `IdentityLens() == IdentityLens()` | ||
4. `ℓ₁ ≍ ℓ₂`, otherwise | ||
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Together, this should make `VarName`s under subsumption a reflexive poset. | ||
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The fundamental requirement for `VarInfo`s is then: | ||
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``` | ||
vi[x ∘ ℓ] == get(vi[x], ℓ) | ||
``` | ||
So we always want the following to work, automatically: | ||
```julia | ||
vi = insert!!(vi, vn, x) | ||
vi[vn] == x | ||
``` | ||
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(the trivial case), and | ||
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```julia | ||
x = set!!(x, ℓ₁, a) | ||
x = set!!(x, ℓ₂, b) | ||
vi = insert!!(vi, vn, x) | ||
vi[vn ∘ ℓ₁] == a | ||
vi[vn ∘ ℓ₂] == b | ||
``` | ||
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since `vn` subsumes both `vn ∘ ℓ₁` and `vn ∘ ℓ₂`. | ||
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Whether the opposite case is supported may depend on the implementation. The most complicated part | ||
is “unification”: | ||
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```julia | ||
vi = insert!!(vi, vn ∘ ℓ₁, a) | ||
vi = insert!!(vi, vn ∘ ℓ₂, b) | ||
get(vi[vn], ℓ₁) == a | ||
get(vi[vn], ℓ₂) == b | ||
``` | ||
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where `vn ∘ ℓ₁` and `vn ∘ ℓ₂` need to be recognized as “children” of a common parent `vn`. |