The math.perm() method

The math.perm() method in Python returns the number of ways to select k elements from n elements, with and without repetition. 🧮

Syntax:

math.perm(n, k)

Where:
n: The number of elements from which k elements are selected.
k: The number of elements that are selected.

In the first example, the method returns the number of ways to select 3 elements from 5 elements. The result is 60 ways. 📊
In the second example, the method returns the number of ways to select 5 elements from 10 elements. The result is 252 ways. 🚀

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Cheat sheet for Scikit-learn: 📚 Scikit-learn is a Python library for machine learning.

📥 Loading Data - downloading and preparing data.
🧼 Preprocessing - standardization, normalization, and feature processing.
🏗️ Create Your Model - creating models for classification, regression, and clustering.
🎯 Model Fitting - training the model on data.
🔮 Prediction - obtaining forecasts.
📊 Evaluate Performance - assessing the quality of the model using various metrics.
🔄 Cross-Validation - checking the model on different samples.
⚙️ Tune Your Model - optimizing parameters using Grid Search and Randomized Search.

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Combining Plots in Matplotlib 📊

In Matplotlib, you can easily combine multiple plots in a single window using the subplot() function. Simply create the necessary plots, specify their layout, add titles, and you'll get a clear visualization for easy data comparison.

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Feature Scaling: Why Feature Scaling Affects Model Training

Feature scaling is often overlooked because it seems like just another data preprocessing step. However, in practice, it often helps models train faster and more stably. Imagine one feature has values ranging from 0 to 1, while another has values ranging from 0 to 10,000. Although both features may be equally important for prediction, it's more difficult for the optimizer to work with such data.

This means it has to take more steps to find a good solution. Additionally, regularization becomes less effective because features with different scales require coefficients of different magnitudes. Let's look at how this looks in a simple example.

Install dependencies:

pip install numpy scikit-learn

Import libraries:

import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import roc_auc_score

Let's create a small synthetic dataset. It will have two features: the first has a normal scale, and the second is about a thousand times larger.

Importantly, both features actually influence the target variable. That is, the only difference between them is the scale.

np.random.seed(42)
x_small = np.random.normal(0, 1, 300)
x_large = np.random.normal(0, 1000, 300)

X = np.vstack([x_small, x_large]).T

y = (x_small + 0.001 * x_large > 0).astype(int)

Now, let's split the data into training and testing sets. We won't scale anything yet—first, let's see how the model behaves on the original data.

X_train, X_test, y_train, y_test = train_test_split(
    X, y,
    test_size=0.3,
    random_state=42,
    stratify=y
)

Let's train a logistic regression model without scaling.

In addition to the model's quality, let's also look at the number of iterations (n_iter_). This metric shows how much work the optimizer had to do to find the coefficients.

model = LogisticRegression()
model.fit(X_train, y_train)

pred = model.predict_proba(X_test)[:, 1]

print("ROC-AUC:", roc_auc_score(y_test, pred))
print("Iterations:", model.n_iter_)

Now, let's scale the features to the same scale using StandardScaler.

It calculates the mean and standard deviation only for the training set and then uses the same values for the test set. This is important because the model should not "peek" at the test data during training.

After this transformation, both features are approximately on the same scale, and it becomes easier for the optimizer to work with them.

scaler = StandardScaler()

X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

Now, let's retrain the model.

We're using the same model, the same data, and the same parameters. The only difference is that the features are now scaled.

model = LogisticRegression()
model.fit(X_train_scaled, y_train)

pred = model.predict_proba(X_test_scaled)[:, 1]

print("ROC-AUC (scaled):", roc_auc_score(y_test, pred))
print("Iterations (scaled):", model.n_iter_)

Most often, the ROC-AUC doesn't change much. However, the number of iterations becomes smaller. This means that the optimizer found a solution faster, and the training was more stable.

🔥 Feature scaling is a simple data preprocessing step that, in many cases, allows the model to train faster and more stably. For logistic regression, SVMs, neural networks, and other algorithms that use numerical optimization, it's best not to skip it.

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Here's a Python tool for accurately extracting text from PDFs and images into Markdown and JSON. 📄✨

It supports tables, formulas, multiple OCR engines (Marker, Surya-OCR, Tesseract) and has built-in personal data removal. 🔒🤖

https://github.com/CatchTheTornado/pdf-extract-api

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Foundations of Applied Mathematics is a free series of four textbooks created for the applied and computational mathematics program at Brigham Young University. 📚

The series includes four volumes:
*   Mathematical Analysis
*   Algorithms, Approximation, and Optimization
*   Uncertainty and Data
*   Dynamics and Control

The series is suitable for upper-level undergraduate and introductory graduate students. It also includes Python lab exercises and practical assignments, connecting mathematical theory with numerical computation, algorithms, data analysis, and scientific applications. 🐍

I particularly appreciate that these are not just theoretical textbooks. The accompanying Python materials help to illustrate how these concepts are applied to real-world computational problems. 💻

https://foundations-of-applied-mathematics.github.io

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A Powerful Alternative to Pandas 🚀

This is an optimized replacement for Pandas that can significantly speed up data processing without requiring major changes to your code. ⚙️

To get started, simply replace a single import:

import fireducks.pandas as pd

Performance Benchmarks demonstrate speed improvements in various use cases. 📈

More: https://colab.research.google.com/drive/1UIokuJ4cytoiVSabRDqcziDXOan8bVua?usp=sharing

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🔖 Learning Data Science through interactive examples

One of the most useful repositories for those who want to better understand machine learning.

It transforms complex concepts into visual experiments: you can study models, change parameters, and immediately see the results.

⛓ Link to GitHub
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A Collection of Machine Learning Libraries for Python 🤖

A large repository containing over 900 libraries and frameworks for machine learning. 📚

All projects are sorted by quality and popularity, which helps you quickly find the best tools for working with AI and ML. ⚙️

Repo: https://github.com/ml-tooling/best-of-ml-python?tab=readme-ov-file#vector-similarity-search-ann

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📚 "Mathematical Methods in Data Science with Python" by Sebastian Roche.

🔗 https://mmids-textbook.github.io

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Cheat sheet for Scapy: creating and configuring packets, working with IP addresses, sending and receiving packets, sniffing traffic, fuzzing, and viewing packet structure. 📦🔍

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Tracking experiments and versioning ML models with MLflow. 🤖

Machine learning development requires saving hyperparameters, metrics, and artifacts for each run to compare results. The MLflow platform logs key metrics and registers trained models in a central registry. We will install MLflow, run a script to log parameters, and register the model.

Let's install the

mlflow

and

scikit-learn

libraries to conduct and log a test experiment. 📦

pip install mlflow scikit-learn

The dependencies for managing ML experiments have been successfully installed. ✅

Now, let's create a Python script called

train.py

that will train a simple model, log metrics, and save it to MLflow. 🐍

import mlflow
from sklearn.ensemble import RandomForestClassifier

mlflow.set_experiment("demo_experiment")
with mlflow.start_run():
    params = {"n_estimators": 100, "max_depth": 5}
    mlflow.log_params(params)
    model = RandomForestClassifier(**params)
    mlflow.log_metric("accuracy", 0.95)
    mlflow.sklearn.log_model(model, "rf_model")

The training script and metric logging are set up and ready to be executed. 🚀

Let's run the training script to capture the results and parameters in the local MLflow storage.

python3 train.py

The experiment has been successfully completed, and the parameters and model artifacts have been saved. 📊

# verification (check for registered runs in MLflow)
mlflow runs list --experiment-name demo_experiment

Expected output:

demo_experiment ... FINISHED

# cleanup (remove the generated directory with artifacts and the script)
rm -rf mlruns train.py

Using MLflow helps avoid chaos when tuning hyperparameters and ensures reproducibility of results. Deploy an MLflow server on a separate host for the entire team to collaborate on the project. 🌐

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