Decision Tree algorithms have at all times fascinated me. They’re straightforward to implement and obtain good outcomes on numerous classification and regression duties. Mixed with boosting, determination bushes are nonetheless state-of-the-art in lots of purposes.
Frameworks similar to sklearn, Lightgbm, xgboost and catboost have performed an excellent job till in the present day. Nonetheless, previously few months, I’ve been lacking help for arrow datasets. Whereas lightgbm has just lately added help for that, it’s nonetheless lacking in most different frameworks. The arrow information format might be an ideal match for determination bushes 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 offers a streaming engine that permits the processing of bigger information than reminiscence. For this reason I made a decision to make use of polars as a backend for constructing a choice tree from scratch.
The aim is to discover some great benefits of utilizing polars for determination bushes by way of reminiscence and runtime. And, in fact, 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 essential factor could be seen within the imports. It was essential 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 technique 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 doable to avoid wasting 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() technique can be utilized on a small instance measurement, and the info must be supplied 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 could be supplied 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, 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]) -> Listing[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: record[str],
target_name: str,
unique_targets: record[int],
depth: int,
) -> dict:
...Becoming the tree
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: Identify 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")
.acquire(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.acquire(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 establish the goal column, the target_name must be supplied.
Polars offers 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’s going to convert the dtype to the smallest doable worth.
The explicit encoding
To encode categorical values, a goal encoding is used. For that, all situations of a categorical function shall be aggregated, and the typical goal worth shall be calculated. Then, the situations are sorted by the typical goal worth, and a rank is assigned. This rank shall 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")
.acquire(streaming=self.streaming)[categorical_column]
)Since it’s doable to supply polars DataFrames and LazyFrames, I take advantage of information.lazy() first. If the given information 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 doable to make sure that the info is processed in the identical manner for LazyFrames and DataFrames and that the acquire() technique can be utilized, which is just obtainable for LazyFrames.
As an example the 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 underneath the Database Contents License.
Right here is an instance of the specific 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() technique, the distinctive goal values are decided.
unique_targets = information.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(information, feature_names, target_name, unique_targets, depth=0)This serves because the final preparation earlier than calling the _build_tree() technique recursively.
Constructing the tree
After the info is ready within the match() technique, the _build_tree() technique known as. That is performed 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: 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 inner nodes for left and proper kids.
:param information: 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 is just not 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 very 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"]) This technique is the guts of constructing the bushes and I’ll clarify it step-by-step. First, when coming into the tactic, it’s checked if the max depth stopping criterion is met.
if self.max_depth is just not 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 higher than the max_depth, a node of the kind leaf shall 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 decided 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 data achieve is used.
To get the data achieve, the guardian entropy and little one entropy must be calculated.
Calculating The Data 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 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 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 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 very 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 particular function worth, it consists of 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 nicely.
After the calculation, the info appears 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 appropriate proportion, we have to know what number of examples now we have on the appropriate 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 depend of examples on the appropriate facet by subtracting the sum of the instance depend from the cumulative sum of the instance depend. Moreover, the guardian proportion is calculated. That is performed by dividing the sum of the goal values counts by the overall depend of examples.
That is the end result information 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 appropriate entropy makes use of the appropriate 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() technique.
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 │
└──────────────┴───────────────┴────────────────┴─────────────────┴────────────────┴───────────────┘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 depend of examples for the function values. The sum of each weighted entropy values is used as little one entropy. To calculate the data achieve, we merely have to subtract the kid entropy from the guardian entropy, as could be seen in Equation 1. The very best function worth is decided by sorting the info by info 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 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 best info achieve. This function worth shall be collected for the age function and must compete in opposition to the opposite options.
Choosing Finest Cut up and Outline Sub Bushes
To pick out the most effective cut up, the best info 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 an inventory of polars DataFrames, that are concatenated and sorted by info achieve.
For the guts illness instance, the info appears 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 the most effective info achieve and thus shall 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 facet. If so, the data achieve is zero. In any other case, we get the function worth with the best info achieve.
if information_gain > 0:
left_mask = information.choose(filter=pl.col(best_params["feature"]) 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 most effective info achieve. The masks is utilized to the guardian information to get the left information body. The negation of the left masks is used to outline the appropriate 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 extra info on the node and shall be seen when plotting the tree together with the opposite info.
When info achieve is zero, a leaf occasion shall be returned. This accommodates the bulk class of the given information.
Make predictions
It’s doable to make predictions in two other 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"]] Right here, the info could be supplied as an iterable of dicts. Every dict accommodates the function names as keys and the function values as values. Through the use of 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]) -> Listing[Union[int, float]]:
"""
Predict technique.
:param information: Polars DataFrame or LazyFrame.
:return: Listing 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"]))
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 an inventory
if isinstance(predictions, pl.LazyFrame):
# Regardless of the execution plans says there is no such thing as a 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() technique. This makes use of the benefits that polars offers by way of parallel processing and reminiscence effectivity.
The info could be supplied 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 about initially of the method. When all predictions are performed, 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 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 as follows:
It achieves a practice and take a look at accuracy of 73% on the given information.
Runtime comparability
One aim of utilizing polars as a backend for determination 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 may’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 by way of reminiscence utilization and runtime. Because the information must be supplied as a numpy array, the reminiscence utilization grows so much. 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 an alternative of getting it in reminiscence makes a distinction to all different frameworks. Nonetheless, the streaming engine remains 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 helpful. Let’s 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: Identify 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 could 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: NoneThe key phrase that’s essential 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 is just not a crucial half, I take away it briefly to discover till what operation streaming is supported.
The following problematic operation is assigning the specific 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 doesn’t help the streaming mode. Even after eradicating the solid, streaming is just not used which could 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: NoneTransferring 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 is just not 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 vary, I’ll cease the exploration right here. It may be concluded that within the determination tree implementation with polars backend, the total potential of streaming can’t be used but since essential operators are nonetheless lacking streaming help. Because the streaming mode is underneath 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 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 determination tree frameworks. The comparability exhibits that this implementation can outperform sklearn by way of runtime and reminiscence utilization. However there are nonetheless different frameworks like lightgbm that present a greater runtime and extra environment friendly processing. There’s lots of potential within the streaming mode when utilizing polars backend. Presently, some operators stop an end-to-end streaming method attributable to a scarcity of streaming help, however that is underneath lively growth. When polars makes progress with that, it’s value revisiting this implementation and evaluating it to different frameworks once more.
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