What is Statistical Representation Learning?
by Stephen M. Walker II, CoFounder / CEO
What is Statistical Representation Learning?
Statistical Representation Learning (SRL) is a set of techniques in machine learning and statistics that allows a system to automatically discover the representations needed for feature detection or classification from raw data. This process replaces manual feature engineering and allows a machine to both learn the features and use them for tasks such as classification.
The origin of learning representations can be traced back to factor analysis and it has become a central theme in deep learning with important applications in computer vision and other fields. Two main themes in representation learning are unsupervised learning of vector representations and learning of both vector and matrix representations.
In the context of statistics, representation learning is about understanding complex data. If the input data are complex, it is desirable to find representations for the data so that they become easier to understand and analyze. Prototypical examples of learning representation in statistics include factor analysis and multidimensional scaling.
In the context of machine learning, a common setup for selfsupervised representation learning of a certain data type (e.g. text, image, audio, video) is to pretrain the model using large datasets of general context, unlabeled data. The result of this is either a set of representations for common data segments (e.g. words) which new data can be broken into, or a neural network able to convert each new data point (e.g. image) into a set of lower dimensional representations.
Statistical Representation Learning is a crucial part of Statistical Learning Theory, a framework for machine learning drawing from the fields of statistics and functional analysis. This theory deals with the statistical inference problem of finding a predictive function from a given set of data.
How is statistical representation learning different from other types of representation learning?
Statistical Representation Learning and other types of Representation Learning, such as those used in Machine Learning, share the common goal of discovering useful representations of input data that can be used for tasks like feature detection or classification. However, they differ in their approaches, assumptions, and focus areas.
Statistical Representation Learning is rooted in statistical methods and theories. It aims to understand complex data by finding representations that make the data easier to analyze. It often uses techniques like factor analysis and multidimensional scaling, and it's a crucial part of Statistical Learning Theory, a framework for machine learning that draws from the fields of statistics and functional analysis.
On the other hand, other types of Representation Learning, particularly those used in Machine Learning, focus more on prediction and generalization from large datasets. These methods often use neural networks and other complex models to learn representations. They are more empirical, focusing on the results and model skill rather than factors like model interpretability.
In Machine Learning, the goal is often to pretrain models using large datasets of general context, unlabeled data, resulting in a set of representations for common data segments or a neural network able to convert each new data point into a set of lower dimensional representations. Machine Learning models are built for providing accurate predictions without explicit programming, and they can capture complex relationships in data.
In contrast, Statistical Representation Learning is more concerned with understanding the underlying structure and relationships in the data. It explicitly specifies a probabilistic model for the data and identifies variables that influence the outcome. It emphasizes the use of statistical methods and is more focused on inference, which is achieved through the creation and fitting of a projectspecific probability model.
What are some examples of statistical representation learning in practice?
Statistical representation learning is a crucial aspect of machine learning and data analysis, where the goal is to find a suitable representation of raw data that makes it easier to perform tasks such as classification or clustering. Here are some examples of statistical representation learning in practice:

Factor Analysis — This is a classic example of statistical representation learning. In factor analysis, multivariate observations, such as test scores on different subjects, are explained by latent factors, such as verbal and analytical intelligence. The latent factors represent the underlying dimensions of the data, providing a simplified view of the original highdimensional data.

Multidimensional Scaling (MDS) — MDS is another prototypical example of learning representation in statistics. It aims to represent highdimensional data in a lowerdimensional space while preserving the distances (or dissimilarities) between the data points. This method is often used in exploratory data analysis to visualize the structure of the data.

Principal Component Analysis (PCA) — PCA is a linear, unsupervised, generative, and global feature learning method. It identifies the directions (principal components) in which the data varies the most and projects the data onto these directions to reduce its dimensionality. PCA is widely used in data analysis and machine learning for tasks such as noise reduction, data compression, and exploratory data analysis.

Linear Discriminant Analysis (LDA) — LDA is a linear, supervised, discriminative, and global method. It aims to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier or, more commonly, for dimensionality reduction before later classification.

Deep Learning — Deep learning models, such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs), learn representations of data by training on large amounts of labeled data. These models automatically learn to extract useful features from raw data, which are then used for tasks such as image classification, speech recognition, and natural language processing.

Representation Learning with Statistical Independence — This approach aims to learn representations that are statistically independent of certain variables to mitigate bias. This is particularly important in fairnessaware machine learning, where the goal is to prevent the learned representations from being biased with respect to sensitive attributes such as gender or race.
What are the advantages and disadvantages of statistical representation learning compared to other types of representation learning?
Statistical representation learning is a method of learning data representations that can be traced back to factor analysis in statistics. It has several advantages and disadvantages compared to other types of representation learning.
Advantages

Interpretability — Statistical models are often transparent and interpretable, making it easy to understand the relationship between variables. This characteristic is beneficial in sectors like healthcare or finance, where interpretability can be crucial for decisionmaking.

Efficiency with Smaller Datasets — Unlike machine learning models, especially deep learning ones, which require vast amounts of data to train effectively, statistical models can provide reliable predictions with smaller datasets. This is advantageous for studies where data collection is expensive or timeconsuming.

WellDefined Relationships — Statistical models can provide clear coefficients for each predictor, making it easy to understand the relationship between variables.
Disadvantages

Overfitting — Statistical learning algorithms can overfit to data, which is not an inherent feature of statistics. Overfitting occurs when a model learns the detail and noise in the training data to the extent that it negatively impacts the performance of the model on new data.

Limitations in Certain Domains — In some specific areas like small molecule property prediction in drug discovery, representation learning has shown multiple limitations, suggesting that continued research and improvements are required.

Robustness to OutofDistribution Data — Some types of statistical representation learning, like contrastive representation learning, may degrade the robustness of representations to outofdistribution data.

Performance with HighDimensional Data — In situations where data has numerous features or variables, machine learning models, especially deep learning networks, can handle this complexity better than traditional statistical models. For instance, image recognition tasks, where an image has thousands of pixels (each being a feature), are better suited for convolutional neural networks.
While statistical representation learning has its advantages, it also has limitations that can be addressed by other types of representation learning. The choice between statistical representation learning and other types depends on the specific requirements of the task at hand, such as the need for interpretability, the size of the dataset, and the complexity of the data.