In this paper we test several approaches to analysing grapheme codebook features for offline writer identification in medieval English scribal manuscripts. Current methods for selecting a codebook typically produce codebooks that perform no better than random grapheme selection, so our aim in this analysis is to identify potential methods of improving codebook selection. Three feature extractio...

Until now we have focused on “typical” outcomes for a random walk in the “central region” of the probability distribution, which contains all of its weight as the number of steps N tend to ∞. For any finite N , now matter how large, however, there is always some chance of finding the random walk outside the central region. Such “extreme events” are not controlled by the Central Limit Theorem, a...

Coupling is a useful tool in the analysis of the mixing time of Markov chains. The basic idea is that a Markov chain that is initialized to some arbitrary distribution can be compared via coupling with another Markov chain that is initialized to the stationary distribution. The two chains then progress simultaneously, and the distance between the two chains at any time indicates how close the r...

The subject of this course is automated learning, or, as we will more often use, machine learning (ML for short). Roughly speaking, we wish to program computers so that they can ”learn”. Before we discuss how machines can learn, or how the process of learning can be automated, let us consider two examples of naturally occurring animal learning. Not surprisingly, some of the most fundamental iss...

This lecture focused on the problem of “Set Cover”, which is known as one of the first proved 21 NP-complete problems[2]. Two formulations will be given and one optimal approximation algorithm based on a greedy strategy is introduced. Further, the problem is generalized to weighted elements and an approximation algorithm derived from an Integer Programming(IP) formulation is presented. 1 Unweig...

The idea of dimension reduction is to find a hyperplane in high-dimensional space such that an objective function [of the data with respect to its projection on the hyperplane] is optimized. In certain cases, we can interpret the dimensions that are obtained; a case study where this has worked is the ideal point model in voting. A commonly used method for dimension reduction is principal compon...