Determination Tree algorithms have at all times fascinated me. They’re straightforward to implement and obtain good outcomes on varied classification and regression duties. Mixed with boosting, choice timber are nonetheless state-of-the-art in lots of purposes.
Frameworks akin to sklearn, Lightgbm, xgboost and catboost have completed an excellent job till right now. Nevertheless, previously 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 could possibly be an ideal match for choice timber because it has a columnar construction optimized for environment friendly knowledge 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 knowledge frameworks. It makes use of the information effectively and avoids copying the information unnecessarily. It additionally gives a streaming engine that permits the processing of bigger knowledge than reminiscence. That is why I made a decision to make use of polars as a backend for constructing a call tree from scratch.
The purpose is to discover the benefits of utilizing polars for choice timber 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 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:
The primary necessary factor might be seen within the imports. It was necessary for me to maintain the import part clear and with as few dependencies as doable. 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 might 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 doable to avoid wasting 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 accessible, predict() and predict_many(). The predict() methodology can be utilized on a small instance dimension, and the information must be supplied as a dict. If we’ve a giant check set, it’s extra environment friendly to make use of the predict_many() methodology. Right here, the information might be supplied as a Polars Dataframe or LazyFrame.
import pickle
from typing import Iterable, Record, 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]) -> Record[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).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(
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 supplied.
Polars gives a handy approach to optimize the reminiscence utilization of the information.
knowledge.choose(pl.all().shrink_dtype())With that, all columns are chosen and evaluated. It is going to convert the dtype to the smallest doable worth.
The specific 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.
(
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 doable to offer polars DataFrames and LazyFrames, I exploit knowledge.lazy() first. If the given knowledge is a DataFrame, it will likely be transformed to a LazyFrame. Whether it is already a LazyFrame, it solely returns self. With that trick, it’s doable to make sure that the information is processed in the identical manner for LazyFrames and DataFrames and that the acquire() methodology can be utilized, which is just accessible for LazyFrames.
As an example the 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 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 information is ready within the match() methodology, the _build_tree() methodology is known as. That is completed 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 one of the best break 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 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 accessible
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 center of constructing the timber and I’ll clarify it step-by-step. First, when getting into the tactic, it’s checked if the max depth stopping criterion is met.
if self.max_depth 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 kind leaf will likely be returned. The worth of the leaf corresponds to the bulk class of the information. 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 rely 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.
Info Acquire as Splitting Standards
To discover a good break up of the information, the knowledge achieve is used.
To get the knowledge achieve, the guardian entropy and baby entropy should be calculated.
Calculating The Info Acquire in Polars
The knowledge 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 overall rely of rows for that function worth is saved as count_examples. Within the final step, the information 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 information 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 information is sorted by the age of years function, and the columns include the rely of class 0, class 1, and the overall rely of examples with the respective function worth.
Within the subsequent step, the cumulative sum over the rely 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 accessible
pl.col("sum_count_examples")
> pl.col("cum_sum_count_examples")
)The instinct behind it’s that when a break up is executed over a particular function worth, it consists of the rely 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 effectively.
After the calculation, the information 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 rely. For the suitable proportion, we have to know what number of examples we’ve on the suitable facet 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 rely of examples on the suitable facet by subtracting the sum of the instance rely from the cumulative sum of the instance rely. Moreover, the guardian proportion is calculated. That is completed by dividing the sum of the goal values counts by the overall rely of examples.
That is the consequence 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 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 suitable entropy makes use of the suitable proportion. For the guardian entropy, the guardian proportion is used. On this implementation, pl.sum_horizontal() is used to calculate the sum of the proportions to utilize doable optimizations from polars. This may also be changed with the python-native sum() methodology.
The information 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 │
└──────────────┴───────────────┴────────────────┴─────────────────┴────────────────┴───────────────┘Nearly 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 rely of examples for the function values. The sum of each weighted entropy values is used as baby entropy. To calculate the knowledge achieve, we merely must subtract the kid entropy from the guardian entropy, as might be seen in Equation 1. One of the best function worth is set by sorting the information by data achieve and deciding on the primary row. It’s appended to an inventory that gathers all one of the best function values from all options.
Earlier than making use of .head(1), the information 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 towards the opposite options.
Choosing Greatest Cut up and Outline Sub Timber
To pick one of the best break 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 center illness instance, the information 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 ┆ lively │
│ 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 one of the best data achieve and thus will likely be chosen for the primary break 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 facet. 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 larger than zero, the sub-trees are outlined. For that, the left masks is outlined utilizing the function worth that resulted in one of the best data achieve. The masks is utilized to the guardian knowledge to get the left knowledge body. The negation of the left masks is used to outline the suitable 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 doable to make predictions in two other 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 information might be supplied 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]) -> Record[Union[int, float]]:
"""
Predict methodology.
:param knowledge: Polars DataFrame or LazyFrame.
:return: Record 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 gives when it comes to parallel processing and reminiscence effectivity.
The information might be supplied as a polars DataFrame or LazyFrame. Equally to the _build_tree() methodology within the coaching course of, a _predict_many() methodology is 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 can’t be preserved with that, a short lived prediction index is about firstly of the method. When all predictions are completed, the unique order is restored with sorting by that index.
Utilizing the classifier on a dataset
A utilization instance for the choice tree classifier might be discovered right here. The choice tree is educated 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 purpose of utilizing polars as a backend for choice timber is to discover the runtime and reminiscence utilization and examine it to different frameworks. For that, I created a reminiscence profiling script that may be discovered right here.
The script compares this implementation, which is known as “efficient-trees” towards 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 opportunity of utilizing arrow datasets some time in the past, the information might be processed effectively. Nevertheless, for the reason that entire dataset nonetheless must be loaded and might’t be streamed, there are nonetheless potential scaling points.
The subsequent 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. For the reason that knowledge must be supplied as a numpy array, the reminiscence utilization grows quite a bit. The runtime might be defined by utilizing just one CPU core. Help for multi-threading or multi-processing doesn’t exist but.
Deep dive: Streaming in polars
As might be seen within the comparability of the frameworks, the opportunity of streaming the information as a substitute of getting it in reminiscence makes a distinction to all different frameworks. Nevertheless, the streaming engine remains to be thought-about an experimental function, and never all operations are suitable with streaming but.
To get a greater understanding of what occurs within the background, a glance into the execution plan is helpful. Let’s soar 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).solid(pl.UInt64).shrink_dtype().alias(target_name)
)The execution plan for knowledge might 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 necessary 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 isn’t a obligatory half, I take away it briefly to discover till what operation streaming is supported.
The subsequent 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]).solid(pl.UInt32) for col in self.categorical_columns]
)The change expression doesn’t help the streaming mode. Even after eradicating the solid, streaming isn’t 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("lively").change([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 isn’t supported anymore. Right here, utilizing pl.col().filter() prevents us from streaming the information.
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 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 choice tree implementation with polars backend, the complete potential of streaming can’t be used but since necessary operators are nonetheless lacking streaming help. For the reason that streaming mode is beneath lively growth, it is likely to be doable 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 submit, I introduced my customized implementation of a call tree utilizing polars as a backend. I confirmed implementation particulars and in contrast it to different choice 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 a variety of potential within the streaming mode when utilizing polars backend. Presently, some operators stop an end-to-end streaming strategy as a result of an absence of streaming help, however that is beneath lively growth. When polars makes progress with that, it’s price revisiting this implementation and evaluating it to different frameworks once more.
