Bayesian

ClusteringA more advanced clustering technique for real world dataPhoto by Tima Miroshnichenko from PexelsIn the real world you will often find that data follows a certain probability distribution. Whether it is a Gaussian (or normal) distribution, Weibull distribution, Poisson distribution, exponential distribution etc., will depend on the specific data.Being aware of which distribution describes your data, or likely best describes your data, allows you to take advantage of that fact, and improve your inference and/or…

Probabilistic Deep LearningThis article belongs to the series “Probabilistic Deep Learning”. This weekly series covers probabilistic approaches to deep learning. The main goal is to extend deep learning models to quantify uncertainty, i.e., know what they do not know.Bayesian Deep Learning is an emerging field that combines the expressiveness and representational power of deep learning with the uncertainty modeling capabilities of Bayesian methods. The integration of these two paradigms offers a principled framework for…

The Continuous Ranked Probability Score compares distributional predictions to ground-truth valuesAn important part of the machine learning workflow is the model evaluation. The process itself can be considered common knowledge: split the data into train and test sets, train the model on the train set, and evaluate its performance on the test set using a score function.The score function (or metric) is a mapping of the ground truth values and their predictions into a single and comparable value . For example, for…

Applying synthetic control with a Bayesian twist to quantify the impact of a tweet (using CausalPy)Image by Tolga Aslantürk at PexelsOctober 2022 brought a lot of novelty to Twitter’s Headquarters in San Francisco (and a sink). Elon Musk, the CEO of Tesla and SpaceX became the new owner and CEO of the company on October 27.Some audiences welcomed the change warmly while others remained skeptical.A day later, on October 28, Musk tweeted “the bird is freed”.How powerful a tweet can be?Let’s see!Image by Laura Tancredi at…

Using and choosing priors in randomized experiments.Cover image, generated by Author using NightCaféRandomized experiments, a.k.a. AB tests, are the established standard in the industry to estimate causal effects. Randomly assigning the treatment (new product, feature, UI, …) to a subset of the population (users, patients, customers, …) we ensure that, on average, the difference in outcomes (revenue, visits, clicks, …) can be attributed to the treatment. Established companies like Booking.com report constantly running…

Probabilistic deep learningThis article belongs to the series “Probabilistic Deep Learning”. This weekly series covers probabilistic approaches to deep learning. The main goal is to extend deep learning models to quantify uncertainty, i.e. know what they do not know.The frequentist approach to statistics is based on the idea of repeated sampling and long-run relative frequency. It involves constructing hypotheses about a population and testing them using sample data. On the other hand, the Bayesian approach is based on…

A comprehensive understanding of the equation MSE = bias² + variance from a Bayesian perspective using examples and simulationsThroughout my machine learning journey, I’ve come across the bias-variance trade-off several times, but I haven’t been able to fully grasp it. However, after adopting a Bayesian perspective, everything started to make sense. In this article, I’ll share my learnings.First, we start with the theory and do a basic example; then we move to a harder example on Bayesian polynomial regression.In any kind…

Here’s how to incorporate uncertainty in your Neural Networks, using a few lines of codePhoto by Towfiqu barbhuiya on UnsplashI have a master's degree in physics and work as an aerospace engineering researcher.Physics and engineering are two distinct sciences that share a desire to understand nature and the ability to model it.The approach of a physicist is more theoretical. The physicist looks at the world and tries to model it in the most accurate way possible. The reality that a physicist models is imperfect and has…

Are you Bayesian or Frequentist?Image generated using Stable DiffusionRegarding the probability school of thought, there are two main approaches: the Bayesian and the frequentist approaches. Both of these approaches have their own strengths and weaknesses, and they are often used in different circumstances to help determine the probability of events.So, what are their differences? Is one better than the other? This is a wrong question to ask; Bayesian thinking is based on the idea that probabilities represent a degree of…

A Case Study of Using Bayesian Inference for Decision MakingImage by the author.One question many of us come across while shopping on Amazon is: how do I compare two ratings? Amazon ratings give us two important pieces of information: the distribution of ratings (how many were five stars, four stars, three stars, two stars or one star) and how many reviews each product received. Comparing distributions can be pretty straightforward: we can compare the average ratings between two products and then decide. How do we…