Decision Tree algorithms have at all times fascinated me. They’re simple to implement and obtain good outcomes on varied classification and regression duties. Mixed with boosting, resolution bushes are nonetheless state-of-the-art in lots of purposes.
Frameworks corresponding to sklearn, Lightgbm, xgboost and catboost have finished an excellent job till at present. Nonetheless, up to now few months, I’ve been lacking help for arrow datasets. Whereas lightgbm has not too long ago added help for that, it’s nonetheless lacking in most different frameworks. The arrow knowledge format might be an ideal match for resolution bushes because it has a columnar construction optimized for environment friendly knowledge processing. Pandas already added help for that and likewise polars makes use of the benefits.
Polars has proven some vital efficiency benefits over most different knowledge frameworks. It makes use of the info effectively and avoids copying the info unnecessarily. It additionally offers a streaming engine that enables the processing of bigger knowledge than reminiscence. This is the reason I made a decision to make use of polars as a backend for constructing a call tree from scratch.
The objective is to discover some great benefits of utilizing polars for resolution bushes when it comes to reminiscence and runtime. And, after all, studying extra about polars, effectively defining expressions, and the streaming engine.
The code for the implementation could be discovered on this repository.
Code overview
To get a primary overview of the code, I’ll present the construction of the DecisionTreeClassifier first:
The primary vital factor could 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 methodology permits to outline if the polars streaming engine needs to be used. Additionally, the max_depth of the tree could be set right here. One other function within the definition of categorical columns. These are dealt with otherwise 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 could 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() methodology can be utilized on a small instance measurement, and the info must be offered as a dict. If we’ve got a giant check set, it’s extra environment friendly to make use of the predict_many() methodology. Right here, the info could be offered as a Polars Dataframe or LazyFrame.
import pickle
from typing import Iterable, Listing, Union
import 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, knowledge: Union[pl.DataFrame, pl.LazyFrame]) -> Union[pl.DataFrame, pl.LazyFrame]:
...
def match(self, knowledge: Union[pl.DataFrame, pl.LazyFrame], target_name: str) -> None:
...
def predict_many(self, knowledge: Union[pl.DataFrame, pl.LazyFrame]) -> Listing[Union[int, float]]:
...
def predict(self, knowledge: Iterable[dict]):
...
def get_majority_class(self, df: Union[pl.DataFrame, pl.LazyFrame], target_name: str) -> str:
...
def _build_tree(
self,
knowledge: Union[pl.DataFrame, pl.LazyFrame],
feature_names: record[str],
target_name: str,
unique_targets: record[int],
depth: int,
) -> dict:
...Becoming the tree
To coach the choice tree classifier, the match() methodology must be used.
def match(self, knowledge: Union[pl.DataFrame, pl.LazyFrame], target_name: str) -> None:
"""
Match methodology to coach the choice tree.
:param knowledge: Polars DataFrame or LazyFrame containing the coaching knowledge.
:param target_name: Identify of the goal column
"""
columns = knowledge.collect_schema().names()
feature_names = [col for col in columns if col != target_name]
# Shrink dtypes
knowledge = knowledge.choose(pl.all().shrink_dtype()).with_columns(
pl.col(target_name).forged(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(
knowledge.lazy()
.group_by(categorical_column)
.agg(pl.col(target_name).imply().alias("avg"))
.kind("avg")
.acquire(streaming=self.streaming)[categorical_column]
)
}
self.categorical_mappings = categorical_mappings
knowledge = self.apply_categorical_mappings(knowledge)
unique_targets = knowledge.choose(target_name).distinctive()
if isinstance(unique_targets, pl.LazyFrame):
unique_targets = unique_targets.acquire(streaming=self.streaming)
unique_targets = unique_targets[target_name].to_list()
self.tree = self._build_tree(knowledge, feature_names, target_name, unique_targets, depth=0)It receives a polars LazyFrame or DataFrame that accommodates all options and the goal column. To establish the goal column, the target_name must be offered.
Polars offers a handy option to optimize the reminiscence utilization of the info.
knowledge.choose(pl.all().shrink_dtype())With that, all columns are chosen and evaluated. It’ll 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 typical goal worth will likely be calculated. Then, the cases are sorted by the typical goal worth, and a rank is assigned. This rank will likely be used because the illustration of the function worth.
(
knowledge.lazy()
.group_by(categorical_column)
.agg(pl.col(target_name).imply().alias("avg"))
.kind("avg")
.acquire(streaming=self.streaming)[categorical_column]
)Since it’s attainable to supply polars DataFrames and LazyFrames, I take advantage of knowledge.lazy() first. If the given knowledge is a DataFrame, it is going to 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 means for LazyFrames and DataFrames and that the acquire() methodology can be utilized, which is simply obtainable for LazyFrames.
For instance the end result of the calculations within the totally 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 printed beneath the Database Contents License.
Right here is an instance of the explicit function illustration for the glucose ranges:
┌──────┬──────┬──────────┐
│ rank ┆ gluc ┆ avg │
│ --- ┆ --- ┆ --- │
│ u32 ┆ i8 ┆ f64 │
╞══════╪══════╪══════════╡
│ 0 ┆ 1 ┆ 0.476139 │
│ 1 ┆ 2 ┆ 0.586319 │
│ 2 ┆ 3 ┆ 0.620972 │
└──────┴──────┴──────────┘For every of the glucose ranges, the chance 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() methodology, the distinctive goal values are decided.
unique_targets = knowledge.choose(target_name).distinctive()
if isinstance(unique_targets, pl.LazyFrame):
unique_targets = unique_targets.acquire(streaming=self.streaming)
unique_targets = unique_targets[target_name].to_list()
self.tree = self._build_tree(knowledge, feature_names, target_name, unique_targets, depth=0)This serves because the final preparation earlier than calling the _build_tree() methodology recursively.
Constructing the tree
After the info is ready within the match() methodology, the _build_tree() methodology known as. That is finished 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() methodology with a depth of zero.
def _build_tree(
self,
knowledge: Union[pl.DataFrame, pl.LazyFrame],
feature_names: record[str],
target_name: str,
unique_targets: record[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 most effective cut up and creates inside nodes for left and proper kids.
:param knowledge: The dataframe to guage.
:param feature_names: Identify of the function columns.
:param target_name: Identify 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 just isn't None and depth >= self.max_depth:
return {"kind": "leaf", "worth": self.get_majority_class(knowledge, target_name)}
# Make knowledge lazy right here to keep away from that it's evaluated in every loop iteration.
knowledge = knowledge.lazy()
# Consider entropy per function:
information_gain_dfs = []
for feature_name in feature_names:
feature_data = knowledge.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(
# Not less than 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 = knowledge.choose(filter=pl.col(best_params["feature"]) <= best_params["feature_value"])
if isinstance(left_mask, pl.LazyFrame):
left_mask = left_mask.acquire(streaming=self.streaming)
left_mask = left_mask["filter"]
# Cut up knowledge
left_df = knowledge.filter(left_mask)
right_df = knowledge.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(knowledge, pl.LazyFrame):
target_distribution = (
knowledge.choose(target_name)
.acquire(streaming=self.streaming)[target_name]
.value_counts()
.kind(target_name)["count"]
.to_list()
)
else:
target_distribution = knowledge[target_name].value_counts().kind(target_name)["count"].to_list()
return {
"kind": "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 {"kind": "leaf", "worth": self.get_majority_class(knowledge, target_name)}This methodology is the guts of constructing the bushes 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 just isn't None and depth >= self.max_depth:
return {"kind": "leaf", "worth": self.get_majority_class(knowledge, target_name)}If the present depth is the same as or higher 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: Identify 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.acquire(streaming=self.streaming)
return majority_class[target_name][0]To get the bulk class, the depend of rows per goal is set by grouping over the goal column and aggregating with len(). The goal occasion, which is current in many of the rows, is returned as the bulk class.
Data Acquire as Splitting Standards
To discover a good cut up of the info, the knowledge achieve is used.
To get the knowledge achieve, the father or mother entropy and little one entropy must be calculated.
Calculating The Data 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 depend of every of the goal values is assigned to it. Moreover, the overall depend 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 guts illness dataset, after the primary calculation step, the info appears to be like like this:
┌───────────────┬───────────────┬───────────────┬────────────────┐
│ feature_value ┆ class_0_count ┆ class_1_count ┆ count_examples │
│ --- ┆ --- ┆ --- ┆ --- │
│ i8 ┆ u32 ┆ u32 ┆ u32 │
╞═══════════════╪═══════════════╪═══════════════╪════════════════╡
│ 29 ┆ 2 ┆ 0 ┆ 2 │
│ 30 ┆ 1 ┆ 0 ┆ 1 │
│ 39 ┆ 1068 ┆ 331 ┆ 1399 │
│ 40 ┆ 975 ┆ 263 ┆ 1238 │
│ 41 ┆ 1052 ┆ 438 ┆ 1490 │
│ … ┆ … ┆ … ┆ … │
│ 60 ┆ 1054 ┆ 1460 ┆ 2514 │
│ 61 ┆ 695 ┆ 1408 ┆ 2103 │
│ 62 ┆ 566 ┆ 1125 ┆ 1691 │
│ 63 ┆ 572 ┆ 1517 ┆ 2089 │
│ 64 ┆ 479 ┆ 1217 ┆ 1696 │
└───────────────┴───────────────┴───────────────┴────────────────┘Right here, the function age_years is processed. Class 0 stands for “no coronary heart illness,” and sophistication 1 stands for “coronary heart illness.” The info is sorted by the age of years function, and the columns include the depend of class 0, class 1, and the overall depend of examples with the respective function worth.
Within the subsequent step, the cumulative sum over the depend of lessons 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(
# Not less than 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 contains the depend of goal values from smaller function values. To have the ability to calculate the proportion, the overall sum of the goal values is calculated. The identical process is repeated for count_examples, the place the cumulative sum and the overall sum are calculated as properly.
After the calculation, the info appears to be like like this:
┌──────────────┬─────────────┬─────────────┬─────────────┬─────────────┬─────────────┬─────────────┐
│ cum_sum_clas ┆ cum_sum_cla ┆ sum_class_0 ┆ sum_class_1 ┆ cum_sum_cou ┆ sum_count_e ┆ feature_val │
│ s_0_count ┆ ss_1_count ┆ _count ┆ _count ┆ nt_examples ┆ xamples ┆ ue │
│ --- ┆ --- ┆ --- ┆ --- ┆ --- ┆ --- ┆ --- │
│ u32 ┆ u32 ┆ u32 ┆ u32 ┆ u32 ┆ u32 ┆ i8 │
╞══════════════╪═════════════╪═════════════╪═════════════╪═════════════╪═════════════╪═════════════╡
│ 3 ┆ 0 ┆ 27717 ┆ 26847 ┆ 3 ┆ 54564 ┆ 29 │
│ 4 ┆ 0 ┆ 27717 ┆ 26847 ┆ 4 ┆ 54564 ┆ 30 │
│ 1097 ┆ 324 ┆ 27717 ┆ 26847 ┆ 1421 ┆ 54564 ┆ 39 │
│ 2090 ┆ 595 ┆ 27717 ┆ 26847 ┆ 2685 ┆ 54564 ┆ 40 │
│ 3155 ┆ 1025 ┆ 27717 ┆ 26847 ┆ 4180 ┆ 54564 ┆ 41 │
│ … ┆ … ┆ … ┆ … ┆ … ┆ … ┆ … │
│ 24302 ┆ 20162 ┆ 27717 ┆ 26847 ┆ 44464 ┆ 54564 ┆ 59 │
│ 25356 ┆ 21581 ┆ 27717 ┆ 26847 ┆ 46937 ┆ 54564 ┆ 60 │
│ 26046 ┆ 23020 ┆ 27717 ┆ 26847 ┆ 49066 ┆ 54564 ┆ 61 │
│ 26615 ┆ 24131 ┆ 27717 ┆ 26847 ┆ 50746 ┆ 54564 ┆ 62 │
│ 27216 ┆ 25652 ┆ 27717 ┆ 26847 ┆ 52868 ┆ 54564 ┆ 63 │
└──────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┴─────────────┘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 depend. For the best proportion, we have to know what number of examples we’ve got on the best aspect for every goal worth. That’s calculated by subtracting the overall sum for the goal worth from the cumulative sum of the goal worth. The identical calculation is used to find out the overall depend of examples on the best aspect by subtracting the sum of the instance depend from the cumulative sum of the instance depend. Moreover, the father or mother proportion is calculated. That is finished by dividing the sum of the goal values counts by the overall depend of examples.
That is the outcome knowledge after this step:
┌───────────┬───────────┬───────────┬───────────┬───┬───────────┬───────────┬───────────┬──────────┐
│ left_prop ┆ left_prop ┆ right_pro ┆ right_pro ┆ … ┆ parent_pr ┆ cum_sum_c ┆ sum_count ┆ feature_ │
│ ortion_cl ┆ ortion_cl ┆ portion_c ┆ portion_c ┆ ┆ oportion_ ┆ ount_exam ┆ _examples ┆ worth │
│ ass_0 ┆ ass_1 ┆ lass_0 ┆ lass_1 ┆ ┆ class_1 ┆ ples ┆ --- ┆ --- │
│ --- ┆ --- ┆ --- ┆ --- ┆ ┆ --- ┆ --- ┆ u32 ┆ i8 │
│ f64 ┆ f64 ┆ f64 ┆ f64 ┆ ┆ f64 ┆ u32 ┆ ┆ │
╞═══════════╪═══════════╪═══════════╪═══════════╪═══╪═══════════╪═══════════╪═══════════╪══════════╡
│ 1.0 ┆ 0.0 ┆ 0.506259 ┆ 0.493741 ┆ … ┆ 0.493714 ┆ 3 ┆ 54564 ┆ 29 │
│ 1.0 ┆ 0.0 ┆ 0.50625 ┆ 0.49375 ┆ … ┆ 0.493714 ┆ 4 ┆ 54564 ┆ 30 │
│ 0.754902 ┆ 0.245098 ┆ 0.499605 ┆ 0.500395 ┆ … ┆ 0.493714 ┆ 1428 ┆ 54564 ┆ 39 │
│ 0.765596 ┆ 0.234404 ┆ 0.492739 ┆ 0.507261 ┆ … ┆ 0.493714 ┆ 2709 ┆ 54564 ┆ 40 │
│ 0.741679 ┆ 0.258321 ┆ 0.486929 ┆ 0.513071 ┆ … ┆ 0.493714 ┆ 4146 ┆ 54564 ┆ 41 │
│ … ┆ … ┆ … ┆ … ┆ … ┆ … ┆ … ┆ … ┆ … │
│ 0.545735 ┆ 0.454265 ┆ 0.333563 ┆ 0.666437 ┆ … ┆ 0.493714 ┆ 44419 ┆ 54564 ┆ 59 │
│ 0.539065 ┆ 0.460935 ┆ 0.305025 ┆ 0.694975 ┆ … ┆ 0.493714 ┆ 46922 ┆ 54564 ┆ 60 │
│ 0.529725 ┆ 0.470275 ┆ 0.297071 ┆ 0.702929 ┆ … ┆ 0.493714 ┆ 49067 ┆ 54564 ┆ 61 │
│ 0.523006 ┆ 0.476994 ┆ 0.282551 ┆ 0.717449 ┆ … ┆ 0.493714 ┆ 50770 ┆ 54564 ┆ 62 │
│ 0.513063 ┆ 0.486937 ┆ 0.296188 ┆ 0.703812 ┆ … ┆ 0.493714 ┆ 52859 ┆ 54564 ┆ 63 │
└───────────┴───────────┴───────────┴───────────┴───┴───────────┴───────────┴───────────┴──────────┘Now that the proportions can be found, the entropy could 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 best entropy makes use of the best 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() methodology.
The info with the entropy values look as follows:
┌──────────────┬───────────────┬────────────────┬─────────────────┬────────────────┬───────────────┐
│ left_entropy ┆ right_entropy ┆ parent_entropy ┆ cum_sum_count_e ┆ sum_count_exam ┆ feature_value │
│ --- ┆ --- ┆ --- ┆ xamples ┆ ples ┆ --- │
│ f64 ┆ f64 ┆ f64 ┆ --- ┆ --- ┆ i8 │
│ ┆ ┆ ┆ u32 ┆ u32 ┆ │
╞══════════════╪═══════════════╪════════════════╪═════════════════╪════════════════╪═══════════════╡
│ -0.0 ┆ 0.999854 ┆ 0.999853 ┆ 3 ┆ 54564 ┆ 29 │
│ -0.0 ┆ 0.999854 ┆ 0.999853 ┆ 4 ┆ 54564 ┆ 30 │
│ 0.783817 ┆ 1.0 ┆ 0.999853 ┆ 1427 ┆ 54564 ┆ 39 │
│ 0.767101 ┆ 0.999866 ┆ 0.999853 ┆ 2694 ┆ 54564 ┆ 40 │
│ 0.808516 ┆ 0.999503 ┆ 0.999853 ┆ 4177 ┆ 54564 ┆ 41 │
│ … ┆ … ┆ … ┆ … ┆ … ┆ … │
│ 0.993752 ┆ 0.918461 ┆ 0.999853 ┆ 44483 ┆ 54564 ┆ 59 │
│ 0.995485 ┆ 0.890397 ┆ 0.999853 ┆ 46944 ┆ 54564 ┆ 60 │
│ 0.997367 ┆ 0.880977 ┆ 0.999853 ┆ 49106 ┆ 54564 ┆ 61 │
│ 0.99837 ┆ 0.859431 ┆ 0.999853 ┆ 50800 ┆ 54564 ┆ 62 │
│ 0.999436 ┆ 0.872346 ┆ 0.999853 ┆ 52877 ┆ 54564 ┆ 63 │
└──────────────┴───────────────┴────────────────┴─────────────────┴────────────────┴───────────────┘Virtually there! The ultimate step is lacking, which is calculating the kid entropy and utilizing that to get the knowledge 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 depend of examples for the function values. The sum of each weighted entropy values is used as little one entropy. To calculate the knowledge achieve, we merely have to subtract the kid entropy from the father or mother entropy, as could be seen in Equation 1. The most effective function worth is set by sorting the info by data achieve and choosing the primary row. It’s appended to an inventory that gathers all the most effective function values from all options.
Earlier than making use of .head(1), the info appears to be like as follows:
┌──────────────────┬────────────────┬───────────────┐
│ information_gain ┆ parent_entropy ┆ feature_value │
│ --- ┆ --- ┆ --- │
│ f64 ┆ f64 ┆ i8 │
╞══════════════════╪════════════════╪═══════════════╡
│ 0.028388 ┆ 0.999928 ┆ 54 │
│ 0.027719 ┆ 0.999928 ┆ 52 │
│ 0.027283 ┆ 0.999928 ┆ 53 │
│ 0.026826 ┆ 0.999928 ┆ 50 │
│ 0.026812 ┆ 0.999928 ┆ 51 │
│ … ┆ … ┆ … │
│ 0.010928 ┆ 0.999928 ┆ 62 │
│ 0.005872 ┆ 0.999928 ┆ 39 │
│ 0.004155 ┆ 0.999928 ┆ 63 │
│ 0.000072 ┆ 0.999928 ┆ 30 │
│ 0.000054 ┆ 0.999928 ┆ 29 │
└──────────────────┴────────────────┴───────────────┘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 Cut up and Outline Sub Bushes
To pick the most effective 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() methodology is used on information_gain_dfs. This evaluates all LazyFrames in parallel, which makes the processing very environment friendly. The result’s an inventory of polars DataFrames, that are concatenated and sorted by data achieve.
For the guts illness instance, the info appears to be like like this:
┌──────────────────┬────────────────┬───────────────┬─────────────┐
│ information_gain ┆ parent_entropy ┆ feature_value ┆ function │
│ --- ┆ --- ┆ --- ┆ --- │
│ f64 ┆ f64 ┆ f64 ┆ str │
╞══════════════════╪════════════════╪═══════════════╪═════════════╡
│ 0.138032 ┆ 0.999909 ┆ 129.0 ┆ ap_hi │
│ 0.09087 ┆ 0.999909 ┆ 85.0 ┆ ap_lo │
│ 0.029966 ┆ 0.999909 ┆ 0.0 ┆ ldl cholesterol │
│ 0.028388 ┆ 0.999909 ┆ 54.0 ┆ age_years │
│ 0.01968 ┆ 0.999909 ┆ 27.435041 ┆ bmi │
│ … ┆ … ┆ … ┆ … │
│ 0.000851 ┆ 0.999909 ┆ 0.0 ┆ energetic │
│ 0.000351 ┆ 0.999909 ┆ 156.0 ┆ top │
│ 0.000223 ┆ 0.999909 ┆ 0.0 ┆ smoke │
│ 0.000098 ┆ 0.999909 ┆ 0.0 ┆ alco │
│ 0.000031 ┆ 0.999909 ┆ 0.0 ┆ gender │
└──────────────────┴────────────────┴───────────────┴─────────────┘Out of all options, the ap_hi (Systolic blood stress) function worth of 129 ends in the most effective 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 instances, information_gain_dfs is likely to be empty, for instance, when all splits end in having solely examples on the left or proper aspect. If that is so, the knowledge achieve is zero. In any other case, we get the function worth with the very best data achieve.
if information_gain > 0:
left_mask = knowledge.choose(filter=pl.col(best_params["feature"]) <= best_params["feature_value"])
if isinstance(left_mask, pl.LazyFrame):
left_mask = left_mask.acquire(streaming=self.streaming)
left_mask = left_mask["filter"]
# Cut up knowledge
left_df = knowledge.filter(left_mask)
right_df = knowledge.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(knowledge, pl.LazyFrame):
target_distribution = (
knowledge.choose(target_name)
.acquire(streaming=self.streaming)[target_name]
.value_counts()
.kind(target_name)["count"]
.to_list()
)
else:
target_distribution = knowledge[target_name].value_counts().kind(target_name)["count"].to_list()
return {
"kind": "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 {"kind": "leaf", "worth": self.get_majority_class(knowledge, target_name)}When the knowledge 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 most effective data achieve. The masks is utilized to the father or mother knowledge to get the left knowledge body. The negation of the left masks is used to outline the best knowledge body. Each left and proper knowledge frames are used to name the _build_tree() methodology 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 knowledge.
Make predictions
It’s attainable to make predictions in two alternative ways. If the enter knowledge is small, the predict() methodology can be utilized.
def predict(self, knowledge: 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 predictionsRight here, the info could 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() methodology, 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, knowledge: Union[pl.DataFrame, pl.LazyFrame]) -> Listing[Union[int, float]]:
"""
Predict methodology.
:param knowledge: Polars DataFrame or LazyFrame.
:return: Listing of predicted goal values.
"""
if self.categorical_mappings:
knowledge = self.apply_categorical_mappings(knowledge)
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"))
knowledge = knowledge.with_row_index("temp_prediction_index")
predictions = _predict_many(self.tree, knowledge).kind("temp_prediction_index").choose(pl.col("prediction"))
# Convert predictions to an inventory
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.acquire(streaming=True)
predictions = predictions["prediction"].to_list()
return predictionsIf a giant instance set needs to be predicted, it’s extra environment friendly to make use of the predict_many() methodology. This makes use of the benefits that polars offers when it comes to parallel processing and reminiscence effectivity.
The info could be offered as a polars DataFrame or LazyFrame. Equally to the _build_tree() methodology within the coaching course of, a _predict_many() methodology known as recursively. All examples within the knowledge 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. For the reason that order cannot be preserved with that, a brief prediction index is about at first of the method. When all predictions are finished, the unique order is restored with sorting by that index.
Utilizing the classifier on a dataset
A utilization instance for the choice tree classifier could be discovered here. The choice tree is skilled on a coronary heart illness dataset. A practice and check 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 practice and check accuracy of 73% on the given knowledge.
Runtime comparability
One objective of utilizing polars as a backend for resolution bushes 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 “efficient-trees” 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 could be processed effectively. Nonetheless, for the reason that complete dataset nonetheless must be loaded and might’t be streamed, there are nonetheless potential scaling points.
The following greatest 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. For the reason that knowledge must be offered as a numpy array, the reminiscence utilization grows rather a lot. The runtime could be defined by utilizing just one CPU core. Assist for multi-threading or multi-processing doesn’t exist but.
Deep dive: Streaming in polars
As could 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-about 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 helpful. Let’s leap again into the coaching course of and get the execution plan for the next operation:
def match(self, knowledge: Union[pl.DataFrame, pl.LazyFrame], target_name: str) -> None:
"""
Match methodology to coach the choice tree.
:param knowledge: Polars DataFrame or LazyFrame containing the coaching knowledge.
:param target_name: Identify of the goal column
"""
columns = knowledge.collect_schema().names()
feature_names = [col for col in columns if col != target_name]
# Shrink dtypes
knowledge = knowledge.choose(pl.all().shrink_dtype()).with_columns(
pl.col(target_name).forged(pl.UInt64).shrink_dtype().alias(target_name)
)The execution plan for knowledge could be created with the next command:
knowledge.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: NoneThe 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. For the reason that dtype shrinking just isn’t a crucial 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, knowledge: Union[pl.DataFrame, pl.LazyFrame]) -> Union[pl.DataFrame, pl.LazyFrame]:
"""
Apply categorical mappings on enter body.
:param knowledge: Polars DataFrame or LazyFrame with categorical columns.
:return: Polars DataFrame or LazyFrame with mapped categorical columns
"""
return knowledge.with_columns(
[pl.col(col).replace(self.categorical_mappings[col]).forged(pl.UInt32) for col in self.categorical_columns]
)The exchange expression doesn’t help the streaming mode. Even after eradicating the forged, streaming just isn’t used which could be seen within the execution plan.
WITH_COLUMNS:
[col("gender").replace([Series, Series]), col("ldl cholesterol").exchange([Series, Series]), col("gluc").exchange([Series, Series]), col("smoke").exchange([Series, Series]), col("alco").exchange([Series, Series]), col("energetic").exchange([Series, Series])]
STREAMING:
DF ["gender", "height", "weight", "ap_hi"]; PROJECT */13 COLUMNS; SELECTION: NoneShifting on, I additionally take away the help for categorical options. What occurs subsequent is the calculation of the knowledge 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 just isn’t 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)]).depend().alias("class_1_count"), col("cardio").filter([(col("cardio")) == (0)]).depend().alias("class_0_count"), col("cardio").depend().alias("count_examples")] BY [col("feature_value")] FROM
STREAMING:
RENAME
easy π 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 complete potential of streaming can’t be used but since vital operators are nonetheless lacking streaming help. For the reason that streaming mode is beneath energetic growth, it is likely to be attainable to run many of the operators and even the entire calculation of the choice tree within the streaming mode sooner or later.
Conclusion
On this weblog put up, I offered my customized implementation of a call tree utilizing polars as a backend. I confirmed implementation particulars and in contrast it to different resolution tree frameworks. The comparability exhibits 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 may be plenty of potential within the streaming mode when utilizing polars backend. At the moment, some operators stop an end-to-end streaming method because of a scarcity of streaming help, however that is beneath energetic growth. When polars makes progress with that, it’s price revisiting this implementation and evaluating it to different frameworks once more.
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