What statistical methods are used in AI R&D?

Statistics is the most important part of any R & D project. Starting from data collection to data cleaning and giving good accuracy in generating any model statistics is required. Descriptive statistics is used for describing the features of population or samples, visualizing the data or to measure central tendency. Where as inferential statistics can be used for generalizing the population by using hypothesis testing. Regression analysis is also a part of statistics. Algorithms like k-means or decision tree for clustering and classifications also need statistics For dimensionality reduction techniques like TSNE, PCA needs statistics. For neural network techniques we need various optimization statistical techniques. Statistics is backbone.

Design of experiments is one of the best tools based on statistical analysis used in the R & D department. By this we can get more information with less experiments so we can finish the optimisation fast.

Interestingly, Data seems to be a key resource for AI R& D , however, data itself is useless without defining your aims and objective, problem statement, A/B testing approach, techniques/methodology, APIs, libraries or modules just to mention a few. The point here is, data itself is meaningless if it is not supported by other resources .

Data serves as the lifeblood of AI, enabling learning and improvement. Without it, AI falters. Data collection, drawing from sources like sensors, surveys, databases, and online platforms, is a vital AI R&D step. Data analysis, involving processing, cleaning, and exploration, reveals patterns and anomalies. Methods like descriptive statistics, inferential statistics, correlation, regression, and visualization are instrumental.

The first step prior to any analysis, is to secure that the data collection is robust. This is ensured by having a data pipeline that: - combines multiple data sources on a timely manner. - facilitates feature engineering and feature experimentation. - does not allow missing values. - takes care of cleaning the data. After securing the above data engineering tasks, data analysis can take place. Having access to a clean dataset allows for quick experimentation and enhances the development of insightful visualizations. This is usually where the domain experts and stakeholders are actively involved in and together with the data analysts are able to steer the developments towards achieving the defined goals.

Machine learning algorithms sometimes seem like magic...but it's important to remember that they aren't! Everything starts with data. Knowing your dataset and understanding the domain are critical because decisions made when building models can determine whether they are accurate and robust or just produce random numbers. Over-fitting is one trap to avoid; the algorithms are so powerful that they can seek out correlations in the noise in your dataset. This will give you models that have brilliant calibration statistics but that fail to predict novel data. Using an independent validation dataset can help to ensure your model isn't over-fitting (but beware; once you have used the independent validation set, it's no longer independent!)

Statistical methods in AI research and development encompass a wide range of techniques. Here's a list of some key methods:. 1. Markov Models: Applied in sequential data analysis. 2. Hidden Markov Models (HMMs): Used in speech and natural language processing. 3. Bayesian Inference: For probabilistic reasoning and parameter estimation. 4. Naive Bayes: Simple probabilistic classifier for text classification. 5.Markov Chain Monte Carlo (MCMC): Sampling method for complex distributions. 6. Reinforcement Learning: Utilizes Markov Decision Processes for agent-based learning. 7. Gaussian Mixture Models: Clustering method based on Gaussian distributions. These methods are foundational for AI research and development.

Most of ML techniques are derived from Statistical Methods. To do AI research strong statistical background is compulsory. It provides various theoretically proven ways to determine the efficiency of ML techniques. Transparency and Interpretability of Statistical Modelling provides it edge for implementation in critical fields like Physics and Medicine where cost of mistakes is very high. In the scientific community, Statistical Modelling is well-established methodology to make inferences from data and to draw conclusions. So, AI researchers validate their research with statistical methods before publishing their research or implementing it at scale.

Machine learning, a subset of AI, empowers computers to learn from data and make predictions or decisions without explicit programming. It relies on mathematical and statistical models trained and validated with data. Key statistical methods include classification, clustering, dimensionality reduction, feature selection, and optimization. These techniques optimize the data-model fit and assess model performance and accuracy.

Regression Analysis: Used for predicting the relationship between variables. Linear regression, logistic regression, and polynomial regression are widely used. Classification: Techniques like Decision Trees, Random Forests, Support Vector Machines (SVM), and Naive Bayes are used for classifying data into predefined categories.

Deep learning, a branch of machine learning, harnesses artificial neural networks to glean insights from vast, intricate data. These networks, akin to the human brain, feature interconnected layers of nodes. Deep learning excels at tasks like image recognition, natural language processing, speech synthesis, and reinforcement learning. Essential statistical techniques include convolution, pooling, activation, regularization, and backpropagation, pivotal for constructing, training, and refining neural networks.

- Check if input features have correlation with target labels . This will tell us if there is a linear relationship between features and labels. Pearson statistical method is one way to that . Neural network is a series of transformations and translations of input to derive an output - Build visualizations to see the individual feature distributions. Find out outliers - Decide scaling methods for features based on their types like log scaling , mean variance scaling - Use statistical methods like percentiles in post processing output probabilities

Deep Neural Networks (DNN): Comprise multiple layers (input, hidden, output) of interconnected nodes (neurons). Activation Functions: Introduce non-linearity into the network, allowing it to learn complex relationships.

Deep learning in particular neural networks are the best universal function approximator right now. It almost learns any arbitrary function with respect to data by repeating back and forth weight propagation (back-prop). These functions can capture nonlinear data since they're the sum of activations of each layer containing a bunch of neurons much like how the human brain works in sync. Depending upon the task in hand like regression, classification, object detection, segmentation, next work prediction. We can adjust the layers(full connection, convolution, rnn, lstm, gru, attention) along with activation function, regularisation(dropout, batchnorm) to create a network and train with an optimisation algorithm.

Mainly, we use these statistical methods : 1. Cosine-similarity 2. Euclidean Distance 3. Manhattan distance 4. Minkowski Distance 5. KL-divergence method

Natural Language Processing has always been the most fascinating frontier to be discovered. As most of the human knowledge is present in words and languages. Because of its complexity earlier NLP had been earlier limited to just applications like sentiment analysis, translations, NER, etc. But with the advent of LLMs (Large Language Models) we have been able to model that complexity in a billion parameter neural net. So I believe now is the right time to capitalise upon the vast knowledge base and discover / re-invent ways to bring about innovative ideas to automate numerous things via machines. Thus freeing the human mind to move to higher realms of knowledge planes.

Neural networks, as a crucial component of deep learning, have enlightened me about the intricate yet highly effective methods for interpreting information. They play a pivotal role in various tasks such as sentiment analysis, text summarization, tokenization, stemming, lemmatization, face recognition and a multitude of other applications. These neural networks harness the power of interconnected layers of artificial neurons to simulate complex human-like information processing, enabling them to tackle a wide array of tasks with remarkable precision and adaptability. I wonder if we can mould it the way how our brain neurons work.

Natural Language Processing (NLP): Sentiment analysis, language translation. Speech Recognition: Automatic speech recognition (ASR). Healthcare: Diagnosis, medical image analysis. Autonomous Vehicles: Image recognition, decision-making

NLP has seen remarkable advancements thanks to cutting-edge statistical methods. Topic modeling techniques like hierarchical Dirichlet processes and neural models uncover hidden themes in unstructured text. Grammar induction approaches, including Bayesian and neural PCFGs, enable unsupervised parsing without labeled data. Word embeddings, such as Bayesian skip-gram and exponential family models, provide interpretable word representations capturing semantics. These techniques lead to sophisticated NLP systems that better understand, generate, and reason with language.

Deep Learning has been one of the best solution for Computer vision for almost a decade, unlike other areas where Deep Learning has found its full use in the last few years such as Generative AI.

From a modern machine learning perspective, the biggest breakthrough has been the impressive performance of convolutional neural network layers. In 2011, it was through the use of CNNs that MNIST digit image recognition saw better-than-human results, and ever since they’ve been a staple of basically every image processing network. If your goal is to learn more about computer vision, I’d recommend looking at training a basic CNN on MNIST digit data yourself, see if you can recreate those record breaking results from more than a decade ago yourself!

Computer Vision: Object detection, image classification, image generation. The process involves analyzing the visual data, extracting relevant features, and using models to classify and localize the objects with bounding boxes.

There is a common misconception that Computer Vision is all about deep learning. In fact, Computer Vision has a rich history of classical algorithms. They would hand-tailor features using essentially filters and thresholding for various applications such as, famously, Optical Character Recognition (OCR). However, difficult applications such as general object detection and facial recognition would need to wait for the advent of Convolutional Neural Networks (CNN) and the historic ImageNet dataset and challenge. Introduced in 2009, deep architectures such as AlexNet gave way to Inception Net and ResNet, which learned to combine multi-scale features and achieve percent-level classification accuracy over its 1000 classes.

Computer vision is a field of AI that enables computers to see and understand visual information. It can be used for applications such as facial recognition, object detection, scene segmentation, and optical character recognition. Some of the statistical methods used in computer vision include edge detection, feature extraction, histogram of oriented gradients, scale-invariant feature transform, and convolutional neural networks. These methods help detect, extract, and classify visual features from images or videos.

Bayesian inference can be contrasted against Frequentist inference, which uses no prior knowledge. An important example to understand the trade-off of these methods is the linear inverse problem, d = Bx + n. It can be shown that the Frequentist view leads to the Maximum Likelihood solution, which only considers the noise covariance matrix N = <nn^T>, where <> denotes an ensemble average. This solution requires that B^TN^{-1}B is invertible, and in that case is the unbiased and minimum variance solution. However, if the system is undetermined, it may be regularized with the help of the prior knowledge, in the form of the signal covariance matrix S. This leads the Wiener filter, which is however, as a filter, always biased to some degree.

Bayesian inference is key in modern AI research and development, providing valuable statistical methods. Bayesian optimization optimizes black-box functions efficiently, with advances like multi-fidelity optimization. Bayesian nonparametric models like Gaussian processes adapt complexity to data - valuable statistical methods for real-world datasets. MCMC methods like Metropolis-Hastings enable approximate inference in complex Bayesian models - widely used statistical methods. Stochastic gradient MCMC and variational inference allow scalable statistical inference. Bayesian neural nets incorporate statistical uncertainty.

Bayesian inference is a powerful statistical method that plays a significant role in AI research and development (R&D) - AI systems frequently grapple with uncertainties, particularly in tasks encompassing prediction, decision-making, and autonomous systems. Bayesian inference offers a robust framework to quantify and manage such uncertainties. - In numerous real-world scenarios, the procurement of large volumes of data is either prohibitively expensive or impractical. Bayesian inference enables researchers to integrate prior knowledge into the model, rendering it invaluable for problems with limited data.

### **Applications of Bayesian Inference** 1. **Probabilistic Programming**: Creating models that incorporate uncertainty by using programming languages designed for statistical modeling. 2. **Causal Inference**: Understanding and predicting the effects of interventions in systems. 3. **Bayesian Optimization**: An efficient method for optimizing objective functions that are expensive to evaluate.

For those interested in learning practical AI, its important to keep in mind that the more you dig into the details, the more complex the math and statistics becomes! But don’t let this discourage you, in the modern day, there are libraries that handle this conplexity for you, and if you want to, you can train ML models without ever knowing a drop of statistics. If you want to dip your toes into some basics though, especially if you’re coming from a background of very limited math experience, I’d recommend first looking at how ML scoring metrics are calculated first. It’s practical, basic, and has real impact, so it’s a good place to start out!

Explainability, validation and bias are critical to ensuring models work. Explainability: Ability to understand a model by looking at coefficients. Techniques like PCA & PLS make this easy. Many others (e.g. neural nets) produce 'black box' models which must be carefully validated. Validation: Assessing the quality of a model using known data. The validation dataset is as important as the calibration dataset (if not more important!) and the less explainable the model, the more you rely on validation. Bias: Systematic error in predictions. This is easily corrected in some applications, but bias has real-world impact on people using the system. Identifying, understanding and managing bias is critical at every stage of the process.

For a successful R&D project consider these additional points: 1. Keep it practical and concise as much as possible. Usually teams are constrained by time and resources, therefore, you need to allocate resources to areas that matter the most. 2. Sometimes, not finding any solution is a worthy conclusion on its own. It proves that the presumptions and expectations were not correct, for example, when your data didn't really have the necessary signal to deliver your expected functionality. 3. After you deliver a product or solution, keep iterating on it and make improvements. Have plans for the next version and next updates already in the pipeline. Most successful projects made it after having multiple shots at a target.

These methods are foundational in AI research and are applied across various domains, including machine learning, deep learning, natural language processing, computer vision, and reinforcement learning.

Not all AIs are machine learning models, but all machine learning models are statistical learning models. In statistical learning, a model uses equations of learned parameters (estimators) to generate conclusions (estimates), based on real-world observations. The estimates can either be it a label (classification), a subgroup(clustering) or a prediction/forecast (regression). These are key aspects to consider when doing R&D in machine/statistical learning: 1. **Bias:** Measures the gap between estimates and the assumed truth in data generation. 2. **Consistency:** Explores if estimators converge to the truth with enough data. 3. **Efficiency:** Examines convergence rates, assessing how quickly estimators reach accurate results.