Resolution tree algorithms have all the time fascinated me. They’re straightforward to implement and obtain good outcomes on numerous classification and regression duties. Mixed with boosting, resolution timber are nonetheless state-of-the-art in lots of purposes.
Frameworks comparable to sklearn, lightgbm, xgboost and catboost have achieved an excellent job till immediately. Nonetheless, previously few months, I’ve been lacking help for arrow datasets. Whereas lightgbm has lately added help for that, it’s nonetheless lacking in most different frameworks. The arrow information format may very well be an ideal match for resolution timber because it has a columnar construction optimized for environment friendly information processing. Pandas already added help for that and in addition polars makes use of the benefits.
Polars has proven some important efficiency benefits over most different information frameworks. It makes use of the info effectively and avoids copying the info unnecessarily. It additionally supplies a streaming engine that enables the processing of bigger information than reminiscence. That is why I made a decision to make use of polars as a backend for constructing a choice tree from scratch.
The objective is to discover the benefits of utilizing polars for resolution timber when it comes to reminiscence and runtime. And, in fact, studying extra about polars, effectively defining expressions, and the streaming engine.
The code for the implementation might be discovered on this repository.
Code overview
To get a primary overview of the code, I’ll present the construction of the DecisionTreeClassifier first:
import pickle
from typing import Iterable, Record, Unionimport polars as pl
class DecisionTreeClassifier:
def __init__(self, streaming=False, max_depth=None, categorical_columns=None):
...
def save_model(self, path: str) -> None:
...
def load_model(self, path: str) -> None:
...
def apply_categorical_mappings(self, information: Union[pl.DataFrame, pl.LazyFrame]) -> Union[pl.DataFrame, pl.LazyFrame]:
...
def match(self, information: Union[pl.DataFrame, pl.LazyFrame], target_name: str) -> None:
...
def predict_many(self, information: Union[pl.DataFrame, pl.LazyFrame]) -> Record[Union[int, float]]:
...
def predict(self, information: Iterable[dict]):
...
def get_majority_class(self, df: Union[pl.DataFrame, pl.LazyFrame], target_name: str) -> str:
...
def _build_tree(
self,
information: Union[pl.DataFrame, pl.LazyFrame],
feature_names: checklist[str],
target_name: str,
unique_targets: checklist[int],
depth: int,
) -> dict:
...
The primary vital factor might be seen within the imports. It was vital for me to maintain the import part clear and with as few dependencies as attainable. This was profitable with solely having dependencies to polars, pickle, and typing.
The init technique permits to outline if the polars streaming engine must be used. Additionally, the max_depth of the tree might be set right here. One other function within the definition of categorical columns. These are dealt with another way than numerical options utilizing a goal encoding.
It’s attainable to save lots of and cargo the choice tree mannequin. It’s represented as a nested dict and might be saved to disk as a pickled file.
The polars magic occurs within the match() and build_tree() strategies. These settle for each LazyFrames and DataFrames to have help for in-memory processing and streaming.
There are two prediction strategies obtainable, predict() and predict_many(). The predict() technique can be utilized on a small instance measurement, and the info must be offered as a dict. If now we have a giant take a look at set, it’s extra environment friendly to make use of the predict_many() technique. Right here, the info might be offered as a polars DataFrame or LazyFrame.
To coach the choice tree classifier, the match() technique must be used.
def match(self, information: Union[pl.DataFrame, pl.LazyFrame], target_name: str) -> None:
"""
Match technique to coach the choice tree.:param information: Polars DataFrame or LazyFrame containing the coaching information.
:param target_name: Title of the goal column
"""
columns = information.collect_schema().names()
feature_names = [col for col in columns if col != target_name]
# Shrink dtypes
information = information.choose(pl.all().shrink_dtype()).with_columns(
pl.col(target_name).solid(pl.UInt64).shrink_dtype().alias(target_name)
)
# Put together categorical columns with goal encoding
if self.categorical_columns:
categorical_mappings = {}
for categorical_column in self.categorical_columns:
categorical_mappings[categorical_column] = {
worth: index
for index, worth in enumerate(
information.lazy()
.group_by(categorical_column)
.agg(pl.col(target_name).imply().alias("avg"))
.kind("avg")
.gather(streaming=self.streaming)[categorical_column]
)
}
self.categorical_mappings = categorical_mappings
information = self.apply_categorical_mappings(information)
unique_targets = information.choose(target_name).distinctive()
if isinstance(unique_targets, pl.LazyFrame):
unique_targets = unique_targets.gather(streaming=self.streaming)
unique_targets = unique_targets[target_name].to_list()
self.tree = self._build_tree(information, feature_names, target_name, unique_targets, depth=0)
It receives a polars LazyFrame or DataFrame that accommodates all options and the goal column. To determine the goal column, the target_name must be offered.
Polars supplies a handy solution to optimize the reminiscence utilization of the info.
information.choose(pl.all().shrink_dtype())
With that, all columns are chosen and evaluated. It can convert the dtype to the smallest attainable worth.
The explicit encoding
To encode categorical values, a goal encoding is used. For that, all cases of a categorical function will likely be aggregated, and the common goal worth will likely be calculated. Then, the cases are sorted by the common goal worth, and a rank is assigned. This rank will likely be used because the illustration of the function worth.
(
information.lazy()
.group_by(categorical_column)
.agg(pl.col(target_name).imply().alias("avg"))
.kind("avg")
.gather(streaming=self.streaming)[categorical_column]
)
Since it’s attainable to offer polars DataFrames and LazyFrames, I exploit information.lazy() first. If the given information is a DataFrame, will probably be transformed to a LazyFrame. Whether it is already a LazyFrame, it solely returns self. With that trick, it’s attainable to make sure that the info is processed in the identical method for LazyFrames and DataFrames and that the gather() technique can be utilized, which is barely obtainable for LazyFrames.
For example the end result of the calculations within the completely different steps of the becoming course of, I apply it to a dataset for coronary heart illness prediction. It may be discovered on Kaggle and is revealed underneath the Database Contents License.
Right here is an instance of the explicit function illustration for the glucose ranges:
ββββββββ¬βββββββ¬βββββββββββ
β rank β gluc β avg β
β --- β --- β --- β
β u32 β i8 β f64 β
ββββββββͺβββββββͺβββββββββββ‘
β 0 β 1 β 0.476139 β
β 1 β 2 β 0.586319 β
β 2 β 3 β 0.620972 β
ββββββββ΄βββββββ΄βββββββββββ
For every of the glucose ranges, the likelihood of getting a coronary heart illness is calculated. That is sorted after which ranked so that every of the degrees is mapped to a rank worth.
Getting the goal values
Because the final a part of the match() technique, the distinctive goal values are decided.
unique_targets = information.choose(target_name).distinctive()
if isinstance(unique_targets, pl.LazyFrame):
unique_targets = unique_targets.gather(streaming=self.streaming)
unique_targets = unique_targets[target_name].to_list()self.tree = self._build_tree(information, feature_names, target_name, unique_targets, depth=0)
This serves because the final preparation earlier than calling the _build_tree() technique recursively.
After the info is ready within the match() technique, the _build_tree() technique known as. That is achieved recursively till a stopping criterion is met, e.g., the max depth of the tree is reached. The primary name is executed from the match() technique with a depth of zero.
def _build_tree(
self,
information: Union[pl.DataFrame, pl.LazyFrame],
feature_names: checklist[str],
target_name: str,
unique_targets: checklist[int],
depth: int,
) -> dict:
"""
Builds the choice tree recursively.
If max_depth is reached, returns a leaf node with the bulk class.
In any other case, finds the perfect cut up and creates inner nodes for left and proper kids.:param information: The dataframe to guage.
:param feature_names: Title of the function columns.
:param target_name: Title of the goal column.
:param unique_targets: distinctive goal values.
:param depth: The present depth of the tree.
:return: A dictionary representing the node.
"""
if self.max_depth will not be None and depth >= self.max_depth:
return {"sort": "leaf", "worth": self.get_majority_class(information, target_name)}
# Make information lazy right here to keep away from that it's evaluated in every loop iteration.
information = information.lazy()
# Consider entropy per function:
information_gain_dfs = []
for feature_name in feature_names:
feature_data = information.choose([feature_name, target_name]).filter(pl.col(feature_name).is_not_null())
feature_data = feature_data.rename({feature_name: "feature_value"})
# No streaming (but)
information_gain_df = (
feature_data.group_by("feature_value")
.agg(
[
pl.col(target_name)
.filter(pl.col(target_name) == target_value)
.len()
.alias(f"class_{target_value}_count")
for target_value in unique_targets
]
+ [pl.col(target_name).len().alias("count_examples")]
)
.kind("feature_value")
.choose(
[
pl.col(f"class_{target_value}_count").cum_sum().alias(f"cum_sum_class_{target_value}_count")
for target_value in unique_targets
]
+ [
pl.col(f"class_{target_value}_count").sum().alias(f"sum_class_{target_value}_count")
for target_value in unique_targets
]
+ [
pl.col("count_examples").cum_sum().alias("cum_sum_count_examples"),
pl.col("count_examples").sum().alias("sum_count_examples"),
]
+ [
# From previous select
pl.col("feature_value"),
]
)
.filter(
# At the least one instance obtainable
pl.col("sum_count_examples")
> pl.col("cum_sum_count_examples")
)
.choose(
[
(pl.col(f"cum_sum_class_{target_value}_count") / pl.col("cum_sum_count_examples")).alias(
f"left_proportion_class_{target_value}"
)
for target_value in unique_targets
]
+ [
(
(pl.col(f"sum_class_{target_value}_count") - pl.col(f"cum_sum_class_{target_value}_count"))
/ (pl.col("sum_count_examples") - pl.col("cum_sum_count_examples"))
).alias(f"right_proportion_class_{target_value}")
for target_value in unique_targets
]
+ [
(pl.col(f"sum_class_{target_value}_count") / pl.col("sum_count_examples")).alias(
f"parent_proportion_class_{target_value}"
)
for target_value in unique_targets
]
+ [
# From previous select
pl.col("cum_sum_count_examples"),
pl.col("sum_count_examples"),
pl.col("feature_value"),
]
)
.choose(
(
-1
* pl.sum_horizontal(
[
(
pl.col(f"left_proportion_class_{target_value}")
* pl.col(f"left_proportion_class_{target_value}").log(base=2)
).fill_nan(0.0)
for target_value in unique_targets
]
)
).alias("left_entropy"),
(
-1
* pl.sum_horizontal(
[
(
pl.col(f"right_proportion_class_{target_value}")
* pl.col(f"right_proportion_class_{target_value}").log(base=2)
).fill_nan(0.0)
for target_value in unique_targets
]
)
).alias("right_entropy"),
(
-1
* pl.sum_horizontal(
[
(
pl.col(f"parent_proportion_class_{target_value}")
* pl.col(f"parent_proportion_class_{target_value}").log(base=2)
).fill_nan(0.0)
for target_value in unique_targets
]
)
).alias("parent_entropy"),
# From earlier choose
pl.col("cum_sum_count_examples"),
pl.col("sum_count_examples"),
pl.col("feature_value"),
)
.choose(
(
pl.col("cum_sum_count_examples") / pl.col("sum_count_examples") * pl.col("left_entropy")
+ (pl.col("sum_count_examples") - pl.col("cum_sum_count_examples"))
/ pl.col("sum_count_examples")
* pl.col("right_entropy")
).alias("child_entropy"),
# From earlier choose
pl.col("parent_entropy"),
pl.col("feature_value"),
)
.choose(
(pl.col("parent_entropy") - pl.col("child_entropy")).alias("information_gain"),
# From earlier choose
pl.col("parent_entropy"),
pl.col("feature_value"),
)
.filter(pl.col("information_gain").is_not_nan())
.kind("information_gain", descending=True)
.head(1)
.with_columns(function=pl.lit(feature_name))
)
information_gain_dfs.append(information_gain_df)
if isinstance(information_gain_dfs[0], pl.LazyFrame):
information_gain_dfs = pl.collect_all(information_gain_dfs, streaming=self.streaming)
information_gain_dfs = pl.concat(information_gain_dfs, how="vertical_relaxed").kind(
"information_gain", descending=True
)
information_gain = 0
if len(information_gain_dfs) > 0:
best_params = information_gain_dfs.row(0, named=True)
information_gain = best_params["information_gain"]
if information_gain > 0:
left_mask = information.choose(filter=pl.col(best_params["feature"]) <= best_params["feature_value"])
if isinstance(left_mask, pl.LazyFrame):
left_mask = left_mask.gather(streaming=self.streaming)
left_mask = left_mask["filter"]
# Break up information
left_df = information.filter(left_mask)
right_df = information.filter(~left_mask)
left_subtree = self._build_tree(left_df, feature_names, target_name, unique_targets, depth + 1)
right_subtree = self._build_tree(right_df, feature_names, target_name, unique_targets, depth + 1)
if isinstance(information, pl.LazyFrame):
target_distribution = (
information.choose(target_name)
.gather(streaming=self.streaming)[target_name]
.value_counts()
.kind(target_name)["count"]
.to_list()
)
else:
target_distribution = information[target_name].value_counts().kind(target_name)["count"].to_list()
return {
"sort": "node",
"function": best_params["feature"],
"threshold": best_params["feature_value"],
"information_gain": best_params["information_gain"],
"entropy": best_params["parent_entropy"],
"target_distribution": target_distribution,
"left": left_subtree,
"proper": right_subtree,
}
else:
return {"sort": "leaf", "worth": self.get_majority_class(information, target_name)}
This technique is the center of constructing the timber and I’ll clarify it step-by-step. First, when getting into the strategy, it’s checked if the max depth stopping criterion is met.
if self.max_depth will not be None and depth >= self.max_depth:
return {"sort": "leaf", "worth": self.get_majority_class(information, target_name)}
If the present depth is the same as or larger than the max_depth, a node of the sort leaf will likely be returned. The worth of the leaf corresponds to the bulk class of the info. That is calculated as follows:
def get_majority_class(self, df: Union[pl.DataFrame, pl.LazyFrame], target_name: str) -> str:
"""
Returns the bulk class of a dataframe.:param df: The dataframe to guage.
:param target_name: Title of the goal column.
:return: majority class.
"""
majority_class = df.group_by(target_name).len().filter(pl.col("len") == pl.col("len").max()).choose(target_name)
if isinstance(majority_class, pl.LazyFrame):
majority_class = majority_class.gather(streaming=self.streaming)
return majority_class[target_name][0]
To get the bulk class, the rely of rows per goal is set by grouping over the goal column and aggregating with len(). The goal occasion, which is current in a lot of the rows, is returned as the bulk class.
Info Acquire as Splitting Standards
To discover a good cut up of the info, the data achieve is used.
To get the data achieve, the father or mother entropy and baby entropy have to be calculated.
A very good rationalization of the interpretation of knowledge achieve might be discovered here.
Calculating The Info Acquire in Polars
The data achieve is calculated for every function worth that’s current in a function column.
information_gain_df = (
feature_data.group_by("feature_value")
.agg(
[
pl.col(target_name)
.filter(pl.col(target_name) == target_value)
.len()
.alias(f"class_{target_value}_count")
for target_value in unique_targets
]
+ [pl.col(target_name).len().alias("count_examples")]
)
.kind("feature_value")
The function values are grouped, and the rely of every of the goal values is assigned to it. Moreover, the full rely of rows for that function worth is saved as count_examples. Within the final step, the info is sorted by feature_value. That is wanted to calculate the splits within the subsequent step.
For the center illness dataset, after the primary calculation step, the info appears to be like like this:
βββββββββββββββββ¬ββββββββββββββββ¬ββββββββββββββββ¬βββββββββββββββββ
β feature_value β class_0_count β class_1_count β count_examples β
β --- β --- β --- β --- β
β i8 β u32 β u32 β u32 β
βββββββββββββββββͺββββββββββββββββͺββββββββββββββββͺβββββββββββββββββ‘
β 29 β 2 β 0 β 2 β
β 30 β 1 β 0 β 1 β
β 39 β 1068 β 331 β 1399 β
β 40 β 975 β 263 β 1238 β
β 41 β 1052 β 438 β 1490 β
β β¦ β β¦ β β¦ β β¦ β
β 60 β 1054 β 1460 β 2514 β
β 61 β 695 β 1408 β 2103 β
β 62 β 566 β 1125 β 1691 β
β 63 β 572 β 1517 β 2089 β
β 64 β 479 β 1217 β 1696 β
βββββββββββββββββ΄ββββββββββββββββ΄ββββββββββββββββ΄βββββββββββββββββ
Right here, the function age_years is processed. Class 0 stands for βno coronary heart illness,β and sophistication 1 stands for βcoronary heart illness.β The info is sorted by the age of years function, and the columns comprise the rely of sophistication 0, class 1, and the full rely of examples with the respective function worth.
Within the subsequent step, the cumulative sum over the rely of courses is calculated for every function worth.
.choose(
[
pl.col(f"class_{target_value}_count").cum_sum().alias(f"cum_sum_class_{target_value}_count")
for target_value in unique_targets
]
+ [
pl.col(f"class_{target_value}_count").sum().alias(f"sum_class_{target_value}_count")
for target_value in unique_targets
]
+ [
pl.col("count_examples").cum_sum().alias("cum_sum_count_examples"),
pl.col("count_examples").sum().alias("sum_count_examples"),
]
+ [
# From previous select
pl.col("feature_value"),
]
)
.filter(
# At the least one instance obtainable
pl.col("sum_count_examples")
> pl.col("cum_sum_count_examples")
)
The instinct behind it’s that when a cut up is executed over a selected function worth, it consists of the rely of goal values from smaller function values. To have the ability to calculate the proportion, the full sum of the goal values is calculated. The identical process is repeated for count_examples, the place the cumulative sum and the full sum are calculated as properly.
After the calculation, the info appears to be like like this:
ββββββββββββββββ¬ββββββββββββββ¬ββββββββββββββ¬ββββββββββββββ¬ββββββββββββββ¬ββββββββββββββ¬ββββββββββββββ
β cum_sum_clas β cum_sum_cla β sum_class_0 β sum_class_1 β cum_sum_cou β sum_count_e β feature_val β
β s_0_count β ss_1_count β _count β _count β nt_examples β xamples β ue β
β --- β --- β --- β --- β --- β --- β --- β
β u32 β u32 β u32 β u32 β u32 β u32 β i8 β
ββββββββββββββββͺββββββββββββββͺββββββββββββββͺββββββββββββββͺββββββββββββββͺββββββββββββββͺββββββββββββββ‘
β 3 β 0 β 27717 β 26847 β 3 β 54564 β 29 β
β 4 β 0 β 27717 β 26847 β 4 β 54564 β 30 β
β 1097 β 324 β 27717 β 26847 β 1421 β 54564 β 39 β
β 2090 β 595 β 27717 β 26847 β 2685 β 54564 β 40 β
β 3155 β 1025 β 27717 β 26847 β 4180 β 54564 β 41 β
β β¦ β β¦ β β¦ β β¦ β β¦ β β¦ β β¦ β
β 24302 β 20162 β 27717 β 26847 β 44464 β 54564 β 59 β
β 25356 β 21581 β 27717 β 26847 β 46937 β 54564 β 60 β
β 26046 β 23020 β 27717 β 26847 β 49066 β 54564 β 61 β
β 26615 β 24131 β 27717 β 26847 β 50746 β 54564 β 62 β
β 27216 β 25652 β 27717 β 26847 β 52868 β 54564 β 63 β
ββββββββββββββββ΄ββββββββββββββ΄ββββββββββββββ΄ββββββββββββββ΄ββββββββββββββ΄ββββββββββββββ΄ββββββββββββββ
Within the subsequent step, the proportions are calculated for every function worth.
.choose(
[
(pl.col(f"cum_sum_class_{target_value}_count") / pl.col("cum_sum_count_examples")).alias(
f"left_proportion_class_{target_value}"
)
for target_value in unique_targets
]
+ [
(
(pl.col(f"sum_class_{target_value}_count") - pl.col(f"cum_sum_class_{target_value}_count"))
/ (pl.col("sum_count_examples") - pl.col("cum_sum_count_examples"))
).alias(f"right_proportion_class_{target_value}")
for target_value in unique_targets
]
+ [
(pl.col(f"sum_class_{target_value}_count") / pl.col("sum_count_examples")).alias(
f"parent_proportion_class_{target_value}"
)
for target_value in unique_targets
]
+ [
# From previous select
pl.col("cum_sum_count_examples"),
pl.col("sum_count_examples"),
pl.col("feature_value"),
]
)
To calculate the proportions, the outcomes from the earlier step can be utilized. For the left proportion, the cumulative sum of every goal worth is split by the cumulative sum of the instance rely. For the correct proportion, we have to know what number of examples now we have on the correct aspect for every goal worth. That’s calculated by subtracting the full sum for the goal worth from the cumulative sum of the goal worth. The identical calculation is used to find out the full rely of examples on the correct aspect by subtracting the sum of the instance rely from the cumulative sum of the instance rely. Moreover, the father or mother proportion is calculated. That is achieved by dividing the sum of the goal values counts by the full rely of examples.
That is the outcome information after this step:
βββββββββββββ¬ββββββββββββ¬ββββββββββββ¬ββββββββββββ¬ββββ¬ββββββββββββ¬ββββββββββββ¬ββββββββββββ¬βββββββββββ
β left_prop β left_prop β right_pro β right_pro β β¦ β parent_pr β cum_sum_c β sum_count β feature_ β
β ortion_cl β ortion_cl β portion_c β portion_c β β oportion_ β ount_exam β _examples β worth β
β ass_0 β ass_1 β lass_0 β lass_1 β β class_1 β ples β --- β --- β
β --- β --- β --- β --- β β --- β --- β u32 β i8 β
β f64 β f64 β f64 β f64 β β f64 β u32 β β β
βββββββββββββͺββββββββββββͺββββββββββββͺββββββββββββͺββββͺββββββββββββͺββββββββββββͺββββββββββββͺβββββββββββ‘
β 1.0 β 0.0 β 0.506259 β 0.493741 β β¦ β 0.493714 β 3 β 54564 β 29 β
β 1.0 β 0.0 β 0.50625 β 0.49375 β β¦ β 0.493714 β 4 β 54564 β 30 β
β 0.754902 β 0.245098 β 0.499605 β 0.500395 β β¦ β 0.493714 β 1428 β 54564 β 39 β
β 0.765596 β 0.234404 β 0.492739 β 0.507261 β β¦ β 0.493714 β 2709 β 54564 β 40 β
β 0.741679 β 0.258321 β 0.486929 β 0.513071 β β¦ β 0.493714 β 4146 β 54564 β 41 β
β β¦ β β¦ β β¦ β β¦ β β¦ β β¦ β β¦ β β¦ β β¦ β
β 0.545735 β 0.454265 β 0.333563 β 0.666437 β β¦ β 0.493714 β 44419 β 54564 β 59 β
β 0.539065 β 0.460935 β 0.305025 β 0.694975 β β¦ β 0.493714 β 46922 β 54564 β 60 β
β 0.529725 β 0.470275 β 0.297071 β 0.702929 β β¦ β 0.493714 β 49067 β 54564 β 61 β
β 0.523006 β 0.476994 β 0.282551 β 0.717449 β β¦ β 0.493714 β 50770 β 54564 β 62 β
β 0.513063 β 0.486937 β 0.296188 β 0.703812 β β¦ β 0.493714 β 52859 β 54564 β 63 β
βββββββββββββ΄ββββββββββββ΄ββββββββββββ΄ββββββββββββ΄ββββ΄ββββββββββββ΄ββββββββββββ΄ββββββββββββ΄βββββββββββ
Now that the proportions can be found, the entropy might be calculated.
.choose(
(
-1
* pl.sum_horizontal(
[
(
pl.col(f"left_proportion_class_{target_value}")
* pl.col(f"left_proportion_class_{target_value}").log(base=2)
).fill_nan(0.0)
for target_value in unique_targets
]
)
).alias("left_entropy"),
(
-1
* pl.sum_horizontal(
[
(
pl.col(f"right_proportion_class_{target_value}")
* pl.col(f"right_proportion_class_{target_value}").log(base=2)
).fill_nan(0.0)
for target_value in unique_targets
]
)
).alias("right_entropy"),
(
-1
* pl.sum_horizontal(
[
(
pl.col(f"parent_proportion_class_{target_value}")
* pl.col(f"parent_proportion_class_{target_value}").log(base=2)
).fill_nan(0.0)
for target_value in unique_targets
]
)
).alias("parent_entropy"),
# From earlier choose
pl.col("cum_sum_count_examples"),
pl.col("sum_count_examples"),
pl.col("feature_value"),
)
For the calculation of the entropy, Equation 2 is used. The left entropy is calculated utilizing the left proportion, and the correct entropy makes use of the correct proportion. For the father or mother entropy, the father or mother proportion is used. On this implementation, pl.sum_horizontal() is used to calculate the sum of the proportions to utilize attainable optimizations from polars. This can be changed with the python-native sum() technique.
The info with the entropy values look as follows:
ββββββββββββββββ¬ββββββββββββββββ¬βββββββββββββββββ¬ββββββββββββββββββ¬βββββββββββββββββ¬ββββββββββββββββ
β left_entropy β right_entropy β parent_entropy β cum_sum_count_e β sum_count_exam β feature_value β
β --- β --- β --- β xamples β ples β --- β
β f64 β f64 β f64 β --- β --- β i8 β
β β β β u32 β u32 β β
ββββββββββββββββͺββββββββββββββββͺβββββββββββββββββͺββββββββββββββββββͺβββββββββββββββββͺββββββββββββββββ‘
β -0.0 β 0.999854 β 0.999853 β 3 β 54564 β 29 β
β -0.0 β 0.999854 β 0.999853 β 4 β 54564 β 30 β
β 0.783817 β 1.0 β 0.999853 β 1427 β 54564 β 39 β
β 0.767101 β 0.999866 β 0.999853 β 2694 β 54564 β 40 β
β 0.808516 β 0.999503 β 0.999853 β 4177 β 54564 β 41 β
β β¦ β β¦ β β¦ β β¦ β β¦ β β¦ β
β 0.993752 β 0.918461 β 0.999853 β 44483 β 54564 β 59 β
β 0.995485 β 0.890397 β 0.999853 β 46944 β 54564 β 60 β
β 0.997367 β 0.880977 β 0.999853 β 49106 β 54564 β 61 β
β 0.99837 β 0.859431 β 0.999853 β 50800 β 54564 β 62 β
β 0.999436 β 0.872346 β 0.999853 β 52877 β 54564 β 63 β
ββββββββββββββββ΄ββββββββββββββββ΄βββββββββββββββββ΄ββββββββββββββββββ΄βββββββββββββββββ΄ββββββββββββββββ
Nearly there! The ultimate step is lacking, which is calculating the kid entropy and utilizing that to get the data achieve.
.choose(
(
pl.col("cum_sum_count_examples") / pl.col("sum_count_examples") * pl.col("left_entropy")
+ (pl.col("sum_count_examples") - pl.col("cum_sum_count_examples"))
/ pl.col("sum_count_examples")
* pl.col("right_entropy")
).alias("child_entropy"),
# From earlier choose
pl.col("parent_entropy"),
pl.col("feature_value"),
)
.choose(
(pl.col("parent_entropy") - pl.col("child_entropy")).alias("information_gain"),
# From earlier choose
pl.col("parent_entropy"),
pl.col("feature_value"),
)
.filter(pl.col("information_gain").is_not_nan())
.kind("information_gain", descending=True)
.head(1)
.with_columns(function=pl.lit(feature_name))
)
information_gain_dfs.append(information_gain_df)
For the kid entropy, the left and proper entropy are weighted by the rely of examples for the function values. The sum of each weighted entropy values is used as baby entropy. To calculate the data achieve, we merely must subtract the kid entropy from the father or mother entropy, as might be seen in Equation 1. The perfect function worth is set by sorting the info by data achieve and deciding on the primary row. It’s appended to a listing that gathers all the perfect function values from all options.
Earlier than making use of .head(1), the info appears to be like as follows:
ββββββββββββββββββββ¬βββββββββββββββββ¬ββββββββββββββββ
β information_gain β parent_entropy β feature_value β
β --- β --- β --- β
β f64 β f64 β i8 β
ββββββββββββββββββββͺβββββββββββββββββͺββββββββββββββββ‘
β 0.028388 β 0.999928 β 54 β
β 0.027719 β 0.999928 β 52 β
β 0.027283 β 0.999928 β 53 β
β 0.026826 β 0.999928 β 50 β
β 0.026812 β 0.999928 β 51 β
β β¦ β β¦ β β¦ β
β 0.010928 β 0.999928 β 62 β
β 0.005872 β 0.999928 β 39 β
β 0.004155 β 0.999928 β 63 β
β 0.000072 β 0.999928 β 30 β
β 0.000054 β 0.999928 β 29 β
ββββββββββββββββββββ΄βββββββββββββββββ΄ββββββββββββββββ
Right here, it may be seen that the age function worth of 54 has the very best data achieve. This function worth will likely be collected for the age function and must compete in opposition to the opposite options.
Deciding on Finest Break up and Outline Sub Bushes
To pick out the perfect cut up, the very best data achieve must be discovered throughout all options.
if isinstance(information_gain_dfs[0], pl.LazyFrame):
information_gain_dfs = pl.collect_all(information_gain_dfs, streaming=self.streaming)information_gain_dfs = pl.concat(information_gain_dfs, how="vertical_relaxed").kind(
"information_gain", descending=True
)
For that, the pl.collect_all() technique is used on information_gain_dfs. This evaluates all LazyFrames in parallel, which makes the processing very environment friendly. The result’s a listing of polars DataFrames, that are concatenated and sorted by data achieve.
For the center illness instance, the info appears to be like like this:
ββββββββββββββββββββ¬βββββββββββββββββ¬ββββββββββββββββ¬ββββββββββββββ
β information_gain β parent_entropy β feature_value β function β
β --- β --- β --- β --- β
β f64 β f64 β f64 β str β
ββββββββββββββββββββͺβββββββββββββββββͺββββββββββββββββͺββββββββββββββ‘
β 0.138032 β 0.999909 β 129.0 β ap_hi β
β 0.09087 β 0.999909 β 85.0 β ap_lo β
β 0.029966 β 0.999909 β 0.0 β ldl cholesterol β
β 0.028388 β 0.999909 β 54.0 β age_years β
β 0.01968 β 0.999909 β 27.435041 β bmi β
β β¦ β β¦ β β¦ β β¦ β
β 0.000851 β 0.999909 β 0.0 β energetic β
β 0.000351 β 0.999909 β 156.0 β top β
β 0.000223 β 0.999909 β 0.0 β smoke β
β 0.000098 β 0.999909 β 0.0 β alco β
β 0.000031 β 0.999909 β 0.0 β gender β
ββββββββββββββββββββ΄βββββββββββββββββ΄ββββββββββββββββ΄ββββββββββββββ
Out of all options, the ap_hi (Systolic blood strain) function worth of 129 ends in the perfect data achieve and thus will likely be chosen for the primary cut up.
information_gain = 0
if len(information_gain_dfs) > 0:
best_params = information_gain_dfs.row(0, named=True)
information_gain = best_params["information_gain"]
In some circumstances, information_gain_dfs could be empty, for instance, when all splits end in having solely examples on the left or proper aspect. If that is so, the data achieve is zero. In any other case, we get the function worth with the very best data achieve.
if information_gain > 0:
left_mask = information.choose(filter=pl.col(best_params["feature"]) <= best_params["feature_value"])
if isinstance(left_mask, pl.LazyFrame):
left_mask = left_mask.gather(streaming=self.streaming)
left_mask = left_mask["filter"]# Break up information
left_df = information.filter(left_mask)
right_df = information.filter(~left_mask)
left_subtree = self._build_tree(left_df, feature_names, target_name, unique_targets, depth + 1)
right_subtree = self._build_tree(right_df, feature_names, target_name, unique_targets, depth + 1)
if isinstance(information, pl.LazyFrame):
target_distribution = (
information.choose(target_name)
.gather(streaming=self.streaming)[target_name]
.value_counts()
.kind(target_name)["count"]
.to_list()
)
else:
target_distribution = information[target_name].value_counts().kind(target_name)["count"].to_list()
return {
"sort": "node",
"function": best_params["feature"],
"threshold": best_params["feature_value"],
"information_gain": best_params["information_gain"],
"entropy": best_params["parent_entropy"],
"target_distribution": target_distribution,
"left": left_subtree,
"proper": right_subtree,
}
else:
return {"sort": "leaf", "worth": self.get_majority_class(information, target_name)}
When the data achieve is bigger than zero, the sub-trees are outlined. For that, the left masks is outlined utilizing the function worth that resulted in the perfect data achieve. The masks is utilized to the father or mother information to get the left information body. The negation of the left masks is used to outline the correct information body. Each left and proper information frames are used to name the _build_tree() technique once more with an elevated depth+1. Because the final step, the goal distribution is calculated. That is used as further data on the node and will likely be seen when plotting the tree together with the opposite data.
When data achieve is zero, a leaf occasion will likely be returned. This accommodates the bulk class of the given information.
It’s attainable to make predictions in two alternative ways. If the enter information is small, the predict() technique can be utilized.
def predict(self, information: Iterable[dict]):
def _predict_sample(node, pattern):
if node["type"] == "leaf":
return node["value"]
if pattern[node["feature"]] <= node["threshold"]:
return _predict_sample(node["left"], pattern)
else:
return _predict_sample(node["right"], pattern)predictions = [_predict_sample(self.tree, sample) for sample in data]
return predictions
Right here, the info might be offered as an iterable of dicts. Every dict accommodates the function names as keys and the function values as values. By utilizing the _predict_sample() technique, the trail within the tree is adopted till a leaf node is reached. This accommodates the category that’s assigned to the respective instance.
def predict_many(self, information: Union[pl.DataFrame, pl.LazyFrame]) -> Record[Union[int, float]]:
"""
Predict technique.:param information: Polars DataFrame or LazyFrame.
:return: Record of predicted goal values.
"""
if self.categorical_mappings:
information = self.apply_categorical_mappings(information)
def _predict_many(node, temp_data):
if node["type"] == "node":
left = _predict_many(node["left"], temp_data.filter(pl.col(node["feature"]) <= node["threshold"]))
proper = _predict_many(node["right"], temp_data.filter(pl.col(node["feature"]) > node["threshold"]))
return pl.concat([left, right], how="diagonal_relaxed")
else:
return temp_data.choose(pl.col("temp_prediction_index"), pl.lit(node["value"]).alias("prediction"))
information = information.with_row_index("temp_prediction_index")
predictions = _predict_many(self.tree, information).kind("temp_prediction_index").choose(pl.col("prediction"))
# Convert predictions to a listing
if isinstance(predictions, pl.LazyFrame):
# Regardless of the execution plans says there isn't any streaming, utilizing streaming right here considerably
# will increase the efficiency and reduces the reminiscence meals print.
predictions = predictions.gather(streaming=True)
predictions = predictions["prediction"].to_list()
return predictions
If a giant instance set must be predicted, it’s extra environment friendly to make use of the predict_many() technique. This makes use of the benefits that polars supplies when it comes to parallel processing and reminiscence effectivity.
The info might be offered as a polars DataFrame or LazyFrame. Equally to the _build_tree() technique within the coaching course of, a _predict_many() technique known as recursively. All examples within the information are filtered into sub-trees till the leaf node is reached. Examples that went the identical path to the leaf node get the identical prediction worth assigned. On the finish of the method, all sub-frames of examples are concatenated once more. Because the order can’t be preserved with that, a brief prediction index is ready firstly of the method. When all predictions are achieved, the unique order is restored with sorting by that index.
A utilization instance for the choice tree classifier might be discovered here. The choice tree is educated on a coronary heart illness dataset. A prepare and take a look at set is outlined to check the efficiency of the implementation. After the coaching, the tree is plotted and saved to a file.
With a max depth of 4, the ensuing tree appears to be like as follows:
It achieves a prepare and take a look at accuracy of 73% on the given information.
One objective of utilizing polars as a backend for resolution timber is to discover the runtime and reminiscence utilization and evaluate it to different frameworks. For that, I created a reminiscence profiling script that may be discovered here.
The script compares this implementation, which known as βefficient-treesβ in opposition to sklearn and lightgbm. For efficient-trees, the lazy streaming variant and non-lazy in-memory variant are examined.
Within the graph, it may be seen that lightgbm is the quickest and most memory-efficient framework. Because it launched the potential of utilizing arrow datasets some time in the past, the info might be processed effectively. Nonetheless, because the entire dataset nonetheless must be loaded and mightβt be streamed, there are nonetheless potential scaling points.
The following finest framework is efficient-trees with out and with streaming. Whereas efficient-trees with out streaming has a greater runtime, the streaming variant makes use of much less reminiscence.
The sklearn implementation achieves the worst outcomes when it comes to reminiscence utilization and runtime. Because the information must be offered as a numpy array, the reminiscence utilization grows so much. The runtime might be defined through the use of just one CPU core. Assist for multi-threading or multi-processing doesnβt exist but.
As might be seen within the comparability of the frameworks, the potential of streaming the info as a substitute of getting it in reminiscence makes a distinction to all different frameworks. Nonetheless, the streaming engine continues to be thought of an experimental function, and never all operations are appropriate with streaming but.
To get a greater understanding of what occurs within the background, a glance into the execution plan is beneficial. Letβs bounce again into the coaching course of and get the execution plan for the next operation:
def match(self, information: Union[pl.DataFrame, pl.LazyFrame], target_name: str) -> None:
"""
Match technique to coach the choice tree.:param information: Polars DataFrame or LazyFrame containing the coaching information.
:param target_name: Title of the goal column
"""
columns = information.collect_schema().names()
feature_names = [col for col in columns if col != target_name]
# Shrink dtypes
information = information.choose(pl.all().shrink_dtype()).with_columns(
pl.col(target_name).solid(pl.UInt64).shrink_dtype().alias(target_name)
)
The execution plan for information might be created with the next command:
information.clarify(streaming=True)
This returns the execution plan for the LazyFrame.
WITH_COLUMNS:
[col("cardio").strict_cast(UInt64).shrink_dtype().alias("cardio")]
SELECT [col("gender").shrink_dtype(), col("height").shrink_dtype(), col("weight").shrink_dtype(), col("ap_hi").shrink_dtype(), col("ap_lo").shrink_dtype(), col("cholesterol").shrink_dtype(), col("gluc").shrink_dtype(), col("smoke").shrink_dtype(), col("alco").shrink_dtype(), col("active").shrink_dtype(), col("cardio").shrink_dtype(), col("age_years").shrink_dtype(), col("bmi").shrink_dtype()] FROM
STREAMING:
DF ["gender", "height", "weight", "ap_hi"]; PROJECT 13/13 COLUMNS; SELECTION: None
The key phrase that’s vital right here is STREAMING. It may be seen that the preliminary dataset loading occurs within the streaming mode, however when shrinking the dtypes, the entire dataset must be loaded into reminiscence. Because the dtype shrinking will not be a essential half, I take away it quickly to discover till what operation streaming is supported.
The following problematic operation is assigning the explicit options.
def apply_categorical_mappings(self, information: Union[pl.DataFrame, pl.LazyFrame]) -> Union[pl.DataFrame, pl.LazyFrame]:
"""
Apply categorical mappings on enter body.:param information: Polars DataFrame or LazyFrame with categorical columns.
:return: Polars DataFrame or LazyFrame with mapped categorical columns
"""
return information.with_columns(
[pl.col(col).replace(self.categorical_mappings[col]).solid(pl.UInt32) for col in self.categorical_columns]
)
The change expression doesnβt help the streaming mode. Even after eradicating the solid, streaming will not be used which might be seen within the execution plan.
WITH_COLUMNS:
[col("gender").replace([Series, Series]), col("ldl cholesterol").change([Series, Series]), col("gluc").change([Series, Series]), col("smoke").change([Series, Series]), col("alco").change([Series, Series]), col("energetic").change([Series, Series])]
STREAMING:
DF ["gender", "height", "weight", "ap_hi"]; PROJECT */13 COLUMNS; SELECTION: None
Transferring on, I additionally take away the help for categorical options. What occurs subsequent is the calculation of the data achieve.
information_gain_df = (
feature_data.group_by("feature_value")
.agg(
[
pl.col(target_name)
.filter(pl.col(target_name) == target_value)
.len()
.alias(f"class_{target_value}_count")
for target_value in unique_targets
]
+ [pl.col(target_name).len().alias("count_examples")]
)
.kind("feature_value")
)
Sadly, already within the first a part of calculating, the streaming mode will not be supported anymore. Right here, utilizing pl.col().filter() prevents us from streaming the info.
SORT BY [col("feature_value")]
AGGREGATE
[col("cardio").filter([(col("cardio")) == (1)]).rely().alias("class_1_count"), col("cardio").filter([(col("cardio")) == (0)]).rely().alias("class_0_count"), col("cardio").rely().alias("count_examples")] BY [col("feature_value")] FROM
STREAMING:
RENAME
easy Ο 2/2 ["gender", "cardio"]
DF ["gender", "height", "weight", "ap_hi"]; PROJECT 2/13 COLUMNS; SELECTION: col("gender").is_not_null()
Since this isn’t really easy to alter, I’ll cease the exploration right here. It may be concluded that within the resolution tree implementation with polars backend, the total potential of streaming canβt be used but since vital operators are nonetheless lacking streaming help. Because the streaming mode is underneath energetic growth, it could be attainable to run a lot of the operators and even the entire calculation of the choice tree within the streaming mode sooner or later.
On this weblog publish, I offered my customized implementation of a choice tree utilizing polars as a backend. I confirmed implementation particulars and in contrast it to different resolution tree frameworks. The comparability reveals that this implementation can outperform sklearn when it comes to runtime and reminiscence utilization. However there are nonetheless different frameworks like lightgbm that present a greater runtime and extra environment friendly processing. There’s plenty of potential within the streaming mode when utilizing polars backend. Presently, some operators forestall an end-to-end streaming method as a result of an absence of streaming help, however that is underneath energetic growth. When polars makes progress with that, it’s value revisiting this implementation and evaluating it to different frameworks once more.
