In recent years, a lot of research has been conducted within the area of causal inference and causal learning. Many methods have been developed to identify the cause-effect pairs in models and have been successfully applied to observational real-world data to determine the direction of causal relationships. Yet in bivariate situations, causal discovery problems remain challenging. One class of such methods, that also allows tackling the bivariate case, is based on Additive Noise Models (ANMs). Unfortunately, one aspect of these methods has not received much attention until now: what is the impact of different noise levels on the ability of these methods to identify the direction of the causal relationship. This work aims to bridge this gap with the help of an empirical study. We test Regression with Subsequent Independence Test (RESIT) using an exhaustive range of models where the level of additive noise gradually changes from 1\% to 10000\% of the causes' noise level (the latter remains fixed). Additionally, the experiments in this work consider several different types of distributions as well as linear and non-linear models. The results of the experiments show that ANMs methods can fail to capture the true causal direction for some levels of noise.

In recent years, the size of datasets have grown exponentially as a result of advances in technology, signal acquisition, and the sophistication of modern day mobile phones and devices. This has enabled researchers, statisticians and machine learning practitioners to build increasingly accurate models as a consequence of larger sample sizes and feature dimensions. Nevertheless, this poses a fundamental challenge to large scale learning as (i) traditional algorithms have computational complexity that scales with the order of the dataset dimensions (ii) the whole dataset has to be stored or transferred on to local RAM as optimisation methods need to return to the data (or a random subset of the data) at subsequent iterations, and (iii) one is vulnerable to malicious attacks of potentially sensitive and personal information as the data needs to be stored or transferred locally. Compressive learning (CL) [1, 2] partially addresses these fundamental challenges by severely compressing the whole dataset into a random representation of fixed size, named a so-called sketch, in a single (or limited) pass of the data prior to learning. Once the sketch is formed, the parameters of the model are inferred solely from the sketch, hence a CL algorithm, for a given task or model, needs never to return to the original dataset, and it can be deleted from memory as a result. At the core of the CL framework [1, 3], is that in general, the size of the sketch does not scale with the dimensions of the dataset, or indeed the data's underlying dimensionality, but instead is driven by the complexity or dimensionality of the task or model of interest.

In recent years, the transformer has established itself as a workhorse in many applications ranging from natural language processing to reinforcement learning. Similarly, Bayesian deep learning has become the gold-standard for uncertainty estimation in safety-critical applications, where robustness and calibration are crucial. Surprisingly, no successful attempts to improve transformer models in terms of predictive uncertainty using Bayesian inference exist. In this work, we study this curiously underpopulated area of Bayesian transformers. We find that weight-space inference in transformers does not work well, regardless of the approximate posterior. We also find that the prior is at least partially at fault, but that it is very hard to find well-specified weight priors for these models. We hypothesize that these problems stem from the complexity of obtaining a meaningful mapping from weight-space to function-space distributions in the transformer. Therefore, moving closer to function-space, we propose a novel method based on the implicit reparameterization of the Dirichlet distribution to apply variational inference directly to the attention weights. We find that this proposed method performs competitively with our baselines.

I do really appreciate these helpful on-hand labs and lectures. Passed the DP-100 in Dec 2020.

The key here is having the best understanding of the problem. Welcome to the ultimate course on Data Science Approach from Scratch!!! This course is your Best Resource for learning the use of Data Science.

SVM is a powerful supervised algorithm that works best on smaller datasets but on complex ones. Support Vector Machine, abbreviated as SVM can be used for both regression and classification tasks, but generally, they work best in classification problems. They were very famous around the time they were created, during the 1990s, and keep on being the go-to method for a high-performing algorithm with a little tuning. By now, I hope you've now mastered Decision Trees, Random Forest, Naïve Bayes, K-nearest neighbor, and Ensemble Modelling techniques. If not, I would suggest you take out a few minutes and read about them as well. In this article, I will explain to you What is SVM, how SVM works, and the math intuition behind this crucial ML algorithm. It is a supervised machine learning problem where we try to find a hyperplane that best separates the two classes. Note: Don't get confused between SVM and logistic regression.

Machine Learning Models play a vital part in Artificial Intelligence. In simple words, they are mathematical representations. In other words, they are the output we receive after training a process. What a machine learning model does is discovers the patterns in a training dataset. In other words, machine learning models map inputs to the outputs of the given dataset.

We saw excellent progress with enterprise acceptance of machine learning across a wide swath of industries and problem domains. In terms of pure research, I had a good time tracking the acceleration of progress in the area of machine learning. In this article, we'll take a tour of my top pick of papers that I found intriguing and useful. In my attempt to stay current with the field's research progress, the directions represented here are very promising. I hope you enjoy the results as much as I have. Overfitting & underfitting and stable training are important challenges in machine learning. Current approaches for these issues are mixup, SamplePairing, and BC learning. This paper states the hypothesis that mixing many images together can be more effective than just two.

We show you how one might code their own linear regression module in Python. Linear regression is the simplest machine learning model you can learn, y

Combining several (sample approximations of) distributions, which we term sub-posteriors, into a single distribution proportional to their product, is a common challenge. For instance, in distributed `big data' problems, or when working under multi-party privacy constraints. Many existing approaches resort to approximating the individual sub-posteriors for practical necessity, then representing the resulting approximate posterior. The quality of the posterior approximation for these approaches is poor when the sub-posteriors fall out-with a narrow range of distributional form. Recently, a Fusion approach has been proposed which finds a direct and exact Monte Carlo approximation of the posterior (as opposed to the sub-posteriors), circumventing the drawbacks of approximate approaches. Unfortunately, existing Fusion approaches have a number of computational limitations, particularly when unifying a large number of sub-posteriors. In this paper, we generalise the theory underpinning existing Fusion approaches, and embed the resulting methodology within a recursive divide-and-conquer sequential Monte Carlo paradigm. This ultimately leads to a competitive Fusion approach, which is robust to increasing numbers of sub-posteriors.