Overview of the Structural Agnostic Model (Structural Agnostic Model) and examples of algorithms and implementations.

Overview of Structural Agnostic Model(SAM)

SAM is one of the methods used in the context of causal inference, which aims to build models without relying on specific assumptions or prior knowledge when inferring causal relationships from data.

Traditional causal inference methods typically use models based on specific causal structures and assumptions, but it is sometimes not clear whether these assumptions are accurate for real data. Assumptions could also introduce bias in causal inference.

SAM is a method for estimating causal effects without relying on such assumptions or prior knowledge, and specifically, it emphasises minimising causal assumptions and constraints when building models to estimate causal effects from data.

SAM can be categorised into two main types of methods.

<Non-parametric methods>

Non-parametric SAM estimates causality without making assumptions about the data. Typical methods include propensity score matching, inverse probability weighting and kernel density estimation, which estimate causal effects based on data and therefore do not require specific assumptions or constraints.

The following sections describe some of the non-parametric methods commonly used in SAM.

• Kernel density estimation: kernel density estimation can be a method for estimating a continuous probability density function without using discrete data representations such as histograms. The method uses a kernel function (usually a Gaussian kernel, for example) centred on each data point to estimate the probability density. Kernel density estimation makes no assumptions about the distribution of the data and is therefore very flexible and applicable to a wide variety of data.
• Non-parametric regression: non-parametric regression is a method for solving regression problems, which does not rely on parametric models such as traditional linear regression, but instead captures local features of the data. This is done by using data from a local neighbourhood to estimate the relationship between the target variable and the characteristics. Typical methods include Locally Weighted Regression and Nadaraya-Watson Regression.
• Non-parametric clustering: non-parametric clustering is a method for hierarchically partitioning data, an approach that does not require a pre-specified number of clusters. Typical methods include hierarchical clustering and methods using dendrograms.
• Non-parametric anomaly detection: non-parametric anomaly detection is a method for detecting data anomalies that does not make a priori assumptions about the normal distribution of the data. Typical methods include approaches that apply kernel density estimation and random cut forests.

<Semiparametric methods>

Semi-parametric SAMs use some parameterised models but allow flexibility in the estimation of causality. Typical methods include Generalised Additive Models (GAMs) and decision tree-based methods, which build more adaptive models for the data by employing flexible functional forms for estimating causal effects.

This section describes the semi-parametric methods used in SAM.

• Semi-parametric regression: semi-parametric regression is a method for solving regression problems, where parametric models such as linear regression are used for some features and non-linear non-parametric regression is applied for others. This allows complex features to be modelled more appropriately while capturing general trends in the data.
• Semi-parametric clustering: semi-parametric clustering is a method of grouping data using clustering techniques, applying parametric models for some clusters and non-parametric methods for others. This eliminates the need to make a priori assumptions about the distribution of data in a particular group and allows for more flexible clustering.
• Semi-parametric anomaly detection: semi-parametric anomaly detection is a method for detecting anomalies in data, using parametric models for some data and applying non-parametric methods for other data. This allows for more flexible modelling when estimating appropriate thresholds for detecting anomalies.

Semi-parametric methods are an important means of achieving flexible modelling in SAMs, while taking into account the characteristics of the data.

SAM is a term used to refer to a model that ignores the structure of specific data and identifies patterns in different data, making this approach useful when the internal structure of the data is unclear or when there is no common structure between the data.

Algorithms used for SAM

There are several algorithms in SAM, but their details are unclear and there is no clearly defined specific algorithm for the structural non-discrimination model. This is because the structural non-discrimination model is a conceptual idea that adopts a different approach to traditional models.

However, the idea is to use a combination of several common machine learning algorithms to realise SAM. Some of the algorithms that may be used for structural non-discriminatory models are described below.

• Clustering algorithms: clustering is a technique for grouping similar data points, and structural non-discrimination models take the approach of ignoring differences between different clusters and attempting to classify data into general patterns.
  Anomie detection: anomie detection is a method for detecting anomalous behaviour in data, whereas structural non-discrimination models may use anomie detection to capture overall characteristics without making a distinction between anomalous data and normal data.
• Dimensionality reduction: dimensionality reduction methods convert high-dimensional data to low dimensions, which can be useful for feature extraction. Structural non-discrimination models may use dimensionality reduction methods to ignore the structure of the data.
• Unsupervised learning: unsupervised learning algorithms are methods that learn using unlabelled data, and the structural non-discriminatory model takes the approach of employing unsupervised learning to capture general features of the data, ignoring the labelling information.

Application examples of Structural Agnostic Modelling (SAM)

Examples of possible applications of SAM include

1. Clustering: SAM can be used to cluster different datasets, e.g. where there are several companies with sales data for different products and each company’s data has a different internal structure, SAM can be used to cluster the sales data of each company, with similar characteristics companies can be grouped into the same group.
2. Anomie detection: SAM can also be used for anomie detection. Anomie detection detects data with behaviour that is different from normal behaviour. For example, when detecting fraudulent transactions in financial transaction data, SAM can be used to identify fraudulent transactions that have a different pattern from normal transactions.
3. Feature selection: SAM can also be applied to feature selection. If a dataset contains several features, some of which do not contribute to the internal structure of the data, SAM can be used to ignore unimportant features and focus on the important ones.
4. Noise reduction: SAM is also useful when the data contain noise. It can capture key patterns without the noise affecting the structure of the data.

Examples of Structural Agnostic Modelling (SAM) implementations.

Structural Agnostic Modelling (SAM) approaches can be useful when model selection and parameter tuning are difficult.

An example of a SAM implementation in Python is given below. The approach presented here is a general one using scikit-learn and statsmodels tools to learn predictive models independent of the structure of the data. Specifically, an example using random forests is given.

Example implementation of SAM using random forests:

import numpy as np
import pandas as pd
from sklearn.ensemble import RandomForestClassifier
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

# Data generation
np.random.seed(42)
n_samples = 1000
n_features = 20

# Generation of features and labels
X = np.random.rand(n_samples, n_features)
y = np.random.randint(0, 2, size=n_samples)  # Two classes of classification problems

# Splitting of data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)

# Creating a model of a random forest.
model = RandomForestClassifier(n_estimators=100, random_state=42)

# Model training
model.fit(X_train, y_train)

# Prediction on test data.
y_pred = model.predict(X_test)

# Assessing the accuracy of the model
accuracy = accuracy_score(y_test, y_pred)
print(f"Accuracy of the model: {accuracy:.2f}")

# Indicate the importance of the feature.
feature_importances = model.feature_importances_
print("Importance of features.:")
for i, importance in enumerate(feature_importances):
    print(f"feature value {i}: {importance:.2f}")

Key points of this approach include the following.

1. Structure-independent: random forests are independent of the structure of the data and can be applied to a wide variety of data sets.
2. High flexibility: models are automatically built based on data features, independent of feature selection and prior model design.
3. Feature importance assessment: after training the model, the importance of features can be assessed, helping to understand which features are important in the data.

The next section describes the application to time series data.

When applying the SAM approach to time series data, tools such as pmdarima and Facebook Prophet can be used to learn predictive models from data without relying on prior model structure.

Facebook Prophet example:

import pandas as pd
from fbprophet import Prophet

# Generation of time series data
np.random.seed(42)
dates = pd.date_range(start='2020-01-01', periods=100)
data = np.sin(np.linspace(0, 10, 100)) + np.random.normal(size=100)
df = pd.DataFrame({'ds': dates, 'y': data})

# Creation of Prophet model.
model = Prophet()
model.fit(df)

# Predicting future data.
future = model.make_future_dataframe(periods=30)
forecast = model.predict(future)

# Plotting the results
model.plot(forecast)

Advantages of using SAM include

• Flexibility: it is independent of the structure of the data and can be used for a variety of data sets.
• High accuracy: better ability to capture complex patterns in the data.
• Automation: minimal model selection and parameter tuning is required.

Thus, using a SAM approach reduces the complexity associated with model design and enables the construction of powerful predictive models that learn automatically from the data.

Structural Agnostic Modelling (SAM) challenges and measures to address them

The following are the main challenges of SAM and the measures taken to address them.

1. reliance on data quantity and quality:

Challenge: SAM builds models from data, which requires large amounts of high-quality data. If the data is small or of low quality, the performance of the model will be degraded.

Solution:
– Data extension: utilise data extension methods and simulations to increase the data set.
– Data pre-processing: ensure thorough data cleaning and pre-processing to provide high quality data.
– Transfer learning: utilise knowledge learned from existing models and datasets and apply it to new tasks.

2. risk of over-learning:

Challenge: flexible model building can lead to over-learning (overfitting). Particularly complex models overfit to training data and perform poorly on new data.

Solution:
– Cross-validation: divide the data into multiple parts and cross-validate to assess the generalisation performance of the model.
– Regularisation: use regularisation techniques to control model complexity and prevent overlearning.
– Ensemble learning: combine multiple models to control over-learning and improve performance.

3. model interpretability:

Challenges: SAM is independent of model structure, making the resulting models complex and difficult to interpret. Poor model interpretability makes it difficult to understand results and make decisions.

Solution:
– Feature importance analysis: assess the importance of features to help understand the model.
– Model visualisation: visualise the outputs of the model and the learning process to improve interpretability.
– Use of simple models: where appropriate, use models that are easy to interpret (e.g. decision trees) to facilitate explanation of results.

4. computational resource requirements:

Challenge: approaches to building models from data are computationally resource-intensive. Computational time and memory consumption are particularly problematic for large data sets and complex models.

Solution:
– Improve computational efficiency: use efficient algorithms and optimisation methods to save computational resources.
– Distributed processing: use distributed processing and cloud computing to process large datasets.
– Sampling: extract samples from large data sets to train and evaluate models.

5. automating model selection:

Challenge: in SAM, the selection of the best model is not always automated. It is important to select appropriate models and hyper-parameters, but this can be difficult.

Solution:
– Hyperparameter tuning: optimise hyperparameters using methods such as grid search and Bayesian optimisation.
– Automatic model selection: use AutoML tools (e.g. Google AutoML, H2O.ai) to automatically select the best models and hyperparameters.

Reference Information and Reference Books

Details of causal inference and causal search are described in “Statistical Causal Inference and Causal Search. See also that contents.

Causal Inference in Statistics” is available as a reference book.

“Causal Inference and Discovery in Python: Unlock the secrets of modern causal machine learning with DoWhy, EconML, PyTorch and more“

“Causal Inference in Python: Applying Causal Inference in the Tech Industry“

“Causal Inference for Data Science“

“The Elements of Statistical Learning: Data Mining, Inference, and Prediction”

“Pattern Recognition and Machine Learning”

“Bayesian Data Analysis”

“Probabilistic Graphical Models: Principles and Techniques”

“Deep Learning“