The objective function presents 2 main problems: 1. how do we minimise it (the answer to this is up for debate and there is lots of interesting research about efficient optimisation of non-convex functions and 2) assuming we can minimise it perfectly, is it the correct thing to be minimising?

It is point 2 which is the focus of this post.

Let’s take the example of square-loss-linear-regression. To do so we train a linear regression model with a square loss . (Where we are taking the inner product of learned weights with a vector of features for each observation to predict the outcome).…

Introduction

The Wisdom of the Crowds, or majority rule and related ideas tend to come up pretty often. Democracy is based (partly) on the majority of people being able to make the correct decision, often you might make decisions in a group of friends based on what the most people want, and it is logical to take into account popular opinion when reasoning on issues where you have imperfect information. On the other hand, of course, there is the Argumentum ad Populum fallacy which states that a popular belief isn’t necessarily true.

This is idea appears also in Applied Machine Learning – ensemble methods such as Random Forests, Gradient Boosted Models (especially XGBoost) and stacking of Neural Networks have resulted in overall more powerful models. This is especially notable in Kaggle competitions, where it is almost always an ensemble model (combination of models) that achieves the best score.…

What is Autodiff?

Autodiff, or Automatic Differentiation, is a method of determining the exact derivative of a function with respect to its inputs. It is widely used in machine learning- in this post I will give an overview of what autodiff is and why it is a useful tool.

The above is not a very helpful definition, so we can compare autodiff first to symbolic differentiation and numerical approximations before going into how it works.

Symbolic differentiation is what we do when we calculate derivatives when we do it by hand, i.e. given a function , we find a new function . This is really good when we want to know how functions behave across all inputs. For example if we had we can find the derivative as and then we can find the derivative of the function for all values of .…

The K-means algorithm

The K-means algorithm is one of the simplest unsupervised learning* algorithms. The aim of the K-means algorithm is, given a set of observations , to group these observations into K different groups in the best way possible (‘best way’ here refers to minimising a loss/cost/objective function).

This is a clustering algorithm, where we want to assign each observation to a group that has other similar observations in it. This could be useful, for example, to split Facebook users into groups that will each be shown a different advertisement.

* unsupervised learning is performed on data without labels, i.e. we have a group of data points (scalar or vector) and we want to find something out about how this data is structured.…

It’s simple but brilliant. They give you something very expensive for free, and you give them something very valuable for free. The brightest minds in machine learning can then potentially earn big money which would be impossible if it weren’t for the beauty of homomorphic encryption.…