Machine Learning: Multiple Logistic Regression

The Machine Learning: Multiple Logistic Regression indicator utilizes a systematic approach to trend forecasting by applying a logistic regression model to multiple normalized technical inputs to generate probability-based buy and sell signals.

Usage

The Usage section focuses on interpreting the machine learning outputs for practical trading decisions. The script processes six distinct technical variables and outputs a probability value between 0 and 1.

• Signal Interpretation: Values closer to 1 indicate a bullish probability, while values closer to 0 indicate a bearish probability. Buy signals are marked by upward arrows (▲) when the probability crosses above 0.5, and sell signals are marked by downward arrows (▼) when it crosses below 0.5.
• Visual Cues: The indicator plots an SMA that changes color based on the regression output (gradient from red to green). Additionally, numeric probability labels are displayed above or below bars to provide granular sentiment data.
• Real-time Monitoring: An on-chart dashboard displays the current state of categorical variables (normalized to 1 or -1) and the weights (coefficients) assigned to them by the model.

Details

The script implements a logistic regression algorithm optimized via Gradient Descent directly within the charting environment.

• Explanatory Variables: The model uses RSI, CCI, DMI, Aroon, EMA, and SuperTrend. These inputs are normalized into categorical variables (typically 1 for bullish alignment and -1 for bearish) to ensure a consistent scale.
• Logistic Function: The core calculation uses a sigmoid function to map the linear combination of inputs and weights into a probability range.
• Optimization: It utilizes a Cross-Entropy Loss function to measure the discrepancy between the model's prediction and the actual price movement (defined by a Z-score of the close).
• Gradient Descent: On every bar, the model updates its internal weights ($b1$ through $b6$) by moving in the opposite direction of the gradient of the loss function, scaled by the user-defined Learning Rate.

Settings

Explanatory Variable Inputs

• Z score Length: Sets the lookback period for the dependent variable calculation (Categorical Y), determining the baseline for "bullish" or "bearish" outcomes.
• RSI/CCI/DMI/AROON/EMA Lengths: These define the lookback periods for each respective technical indicator used as an input variable.
• SuperTrend Factor/ATR Period: Controls the sensitivity and lookback of the SuperTrend component of the model.

Regression Coefficients (Weights)

• $\beta1$ - $\beta6$: Initial weight values assigned to RSI, CCI, DMI, Aroon, EMA, and SuperTrend. These serve as the starting point before the gradient descent optimization begins adjusting them based on historical performance.

Learning Step

• Step of learning (lr): Controls the size of the weight adjustments during optimization. A higher rate allows for faster adaptation to market changes but may cause instability, while a lower rate is more stable but reacts slower.

FAQ

How do I interpret the probability labels? The labels represent the logistic regression output. A value of 0.8 means the model calculates an 80% probability of a bullish state based on the current configuration of technical inputs and learned weights.

What does the table in the corner show? The table provides transparency into the "black box." It shows whether each indicator is currently in a bullish (1) or bearish (-1) state and the specific weight ($\beta$) the model is currently applying to that indicator.

How can I access this tool? You can get access on the LuxAlgo Library for charting platforms like TradingView, MetaTrader (MT4/MT5), and NinjaTrader for free.