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Looking at the answer of @happyfish the code below is an overkill...

Here we find the positions corresponding in the values:

pos = Position[vals, _?NumberQ, \[Infinity]]

Here we find the dimensions corresponding to the positions:

posToDims = MapThread[Part, {dims, #}] & /@ pos

Here we make Trie records from the dimensions and the values:

t = MapThread[
  Function[{d, p}, Append[d, vals[[Sequence @@ p]]]], {posToDims, pos}, 1]

Here we make the trie:

res = makeTreeAssoc[t]

Finally, we remove the redundant <|{}->{}|> (coming from Shifrin's original implementation):

res /. <|k_ -> <|{} -> {}|>|> :> k

(* {"New York City" -> <|"Terrace house" -> <|"Two bed" -> \
    <|"2016" -> 0., "2017" -> 633.25|>, 
 "Three bed" -> <|"2016" -> 642.96, "2017" -> 677.34|>|>, 
 "Apartment" -> <|"Two bed" -> <|"2016" -> 591.56, 
   "2017" -> 632.45|>, 
 "Three bed" -> <|"2016" -> 634.9, "2017" -> 715.6|>|>|>} *)

Definitions

Here is a small change of the original definitions are given in this answer:

ClearAll[makeTreeAssoc];
makeTreeAssoc[wrds_ /; MemberQ[wrds, {}]] := 
  Prepend[makeTreeAssoc[DeleteCases[wrds, {}]], {} -> {}];
makeTreeAssoc[wrds_] := 
 Reap[If[# =!= {}, Sow[Rest[#], First@#]] & /@ 
    wrds, _, #1 -> Association@makeTreeAssoc[#2] &][[2]]

(I was tempted to give an answer with one of my Trie packages, but luckily Leonid Shifrin has provided a concise implementation of Tries using core Association functionalities.)

Looking at the answer of @happyfish the code below is overkill...

Here we find the positions corresponding in the values:

pos = Position[vals, _?NumberQ, \[Infinity]]

Here we find the dimensions corresponding to the positions:

posToDims = MapThread[Part, {dims, #}] & /@ pos

Here we make Trie records from the dimensions and the values:

t = MapThread[
  Function[{d, p}, Append[d, vals[[Sequence @@ p]]]], {posToDims, pos}, 1]

Here we make the trie:

res = makeTreeAssoc[t]

Finally, we remove the redundant <|{}->{}|> (coming from Shifrin's original implementation):

res /. <|k_ -> <|{} -> {}|>|> :> k

(* {"New York City" -> <|"Terrace house" -> <|"Two bed" -> \
    <|"2016" -> 0., "2017" -> 633.25|>, 
 "Three bed" -> <|"2016" -> 642.96, "2017" -> 677.34|>|>, 
 "Apartment" -> <|"Two bed" -> <|"2016" -> 591.56, 
   "2017" -> 632.45|>, 
 "Three bed" -> <|"2016" -> 634.9, "2017" -> 715.6|>|>|>} *)

Definitions

Here is a small change of the original definitions are given in this answer:

ClearAll[makeTreeAssoc];
makeTreeAssoc[wrds_ /; MemberQ[wrds, {}]] := 
  Prepend[makeTreeAssoc[DeleteCases[wrds, {}]], {} -> {}];
makeTreeAssoc[wrds_] := 
 Reap[If[# =!= {}, Sow[Rest[#], First@#]] & /@ 
    wrds, _, #1 -> Association@makeTreeAssoc[#2] &][[2]]

(I was tempted to give an answer with one of my Trie packages, but luckily Leonid Shifrin has provided a concise implementation of Tries using core Association functionalities.)

Looking at the answer of @happyfish the code below is an overkill...

Here we find the positions corresponding in the values:

pos = Position[vals, _?NumberQ, \[Infinity]]

Here we find the dimensions corresponding to the positions:

posToDims = MapThread[Part, {dims, #}] & /@ pos

Here we make Trie records from the dimensions and the values:

t = MapThread[
  Function[{d, p}, Append[d, vals[[Sequence @@ p]]]], {posToDims, pos}, 1]

Here we make the trie:

res = makeTreeAssoc[t]

Finally, we remove the redundant <|{}->{}|> (coming from Shifrin's original implementation):

res /. <|k_ -> <|{} -> {}|>|> :> k

(* {"New York City" -> <|"Terrace house" -> <|"Two bed" -> \
    <|"2016" -> 0., "2017" -> 633.25|>, 
 "Three bed" -> <|"2016" -> 642.96, "2017" -> 677.34|>|>, 
 "Apartment" -> <|"Two bed" -> <|"2016" -> 591.56, 
   "2017" -> 632.45|>, 
 "Three bed" -> <|"2016" -> 634.9, "2017" -> 715.6|>|>|>} *)

Definitions

Here is a small change of the original definitions are given in this answer:

ClearAll[makeTreeAssoc];
makeTreeAssoc[wrds_ /; MemberQ[wrds, {}]] := 
  Prepend[makeTreeAssoc[DeleteCases[wrds, {}]], {} -> {}];
makeTreeAssoc[wrds_] := 
 Reap[If[# =!= {}, Sow[Rest[#], First@#]] & /@ 
    wrds, _, #1 -> Association@makeTreeAssoc[#2] &][[2]]

(I was tempted to give an answer with one of my Trie packages, but luckily Leonid Shifrin has provided a concise implementation of Tries using core Association functionalities.)

1
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Looking at the answer of @happyfish the code below is overkill...

Here we find the positions corresponding in the values:

pos = Position[vals, _?NumberQ, \[Infinity]]

Here we find the dimensions corresponding to the positions:

posToDims = MapThread[Part, {dims, #}] & /@ pos

Here we make Trie records from the dimensions and the values:

t = MapThread[
  Function[{d, p}, Append[d, vals[[Sequence @@ p]]]], {posToDims, pos}, 1]

Here we make the trie:

res = makeTreeAssoc[t]

Finally, we remove the redundant <|{}->{}|> (coming from Shifrin's original implementation):

res /. <|k_ -> <|{} -> {}|>|> :> k

(* {"New York City" -> <|"Terrace house" -> <|"Two bed" -> \
    <|"2016" -> 0., "2017" -> 633.25|>, 
 "Three bed" -> <|"2016" -> 642.96, "2017" -> 677.34|>|>, 
 "Apartment" -> <|"Two bed" -> <|"2016" -> 591.56, 
   "2017" -> 632.45|>, 
 "Three bed" -> <|"2016" -> 634.9, "2017" -> 715.6|>|>|>} *)

Definitions

Here is a small change of the original definitions are given in this answer:

ClearAll[makeTreeAssoc];
makeTreeAssoc[wrds_ /; MemberQ[wrds, {}]] := 
  Prepend[makeTreeAssoc[DeleteCases[wrds, {}]], {} -> {}];
makeTreeAssoc[wrds_] := 
 Reap[If[# =!= {}, Sow[Rest[#], First@#]] & /@ 
    wrds, _, #1 -> Association@makeTreeAssoc[#2] &][[2]]

(I was tempted to give an answer with one of my Trie packages, but luckily Leonid Shifrin has provided a concise implementation of Tries using core Association functionalities.)