This is an exciting opportunity for a researcher at post-doctoral level with experience of machine learning and data mining. You will work with senior data scientists based within the local NHS trusts, the University of Manchester Health eResearch Centre, and Health Innovation Manchester to automate data extraction of predetermined features for all patients diagnosed with ovarian and colorectal cancer in the conurbation. Machine learning tools including neural networks, support vector machines and naïve Bayes algorithms will be refined and tested using the datasets accrued and optimised for clinical practice. Accuracy of prediction will be assessed using predefined criteria. Knowledge of cancer treatment would be useful but is not essential, as the team has extensive expertise in this area.

Topic models have emerged as fundamental tools in unsupervised machine learning. Most modern topic modeling algorithms take a probabilistic view and derive inference algorithms based on Latent Dirichlet Allocation (LDA) or its variants. In contrast, we study topic modeling as a combinatorial optimization problem, and propose a new objective function derived from LDA by passing to the small-variance limit. We minimize the derived objective by using ideas from combinatorial optimization, which results in a new, fast, and high-quality topic modeling algorithm. In particular, we show that our results are competitive with popular LDA-based topic modeling approaches, and also discuss the (dis)similarities between our approach and its probabilistic counterparts.

Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference has proven to be more challenging. Here we take a first step towards provable inference in topic models. We leverage a property of topic models that enables us to construct simple linear estimators for the unknown topic proportions that have small variance, and consequently can work with short documents. Our estimators also correspond to finding an estimate around which the posterior is well-concentrated. We show lower bounds that for shorter documents it can be information theoretically impossible to find the hidden topics. Finally, we give empirical results that demonstrate that our algorithm works on realistic topic models. It yields good solutions on synthetic data and runs in time comparable to a {\em single} iteration of Gibbs sampling.

We learn the structure of a Markov Network between two groups of random variables from joint observations. Since modelling and learning the full MN structure may be hard, learning the links between two groups directly may be a preferable option. We introduce a novel concept called the \emph{partitioned ratio} whose factorization directly associates with the Markovian properties of random variables across two groups. A simple one-shot convex optimization procedure is proposed for learning the \emph{sparse} factorizations of the partitioned ratio and it is theoretically guaranteed to recover the correct inter-group structure under mild conditions. The performance of the proposed method is experimentally compared with the state of the art MN structure learning methods using ROC curves. Real applications on analyzing bipartisanship in US congress and pairwise DNA/time-series alignments are also reported.

We propose a robust classifier to predict buying intentions based on user behaviour within a large e-commerce website. In this work we compare traditional machine learning techniques with the most advanced deep learning approaches. We show that both Deep Belief Networks and Stacked Denoising auto-Encoders achieved a substantial improvement by extracting features from high dimensional data during the pre-train phase. They prove also to be more convenient to deal with severe class imbalance.

The Naive Bayes classifier is a simple classifier that is often used as a baseline for comparison with more complex classifiers. We will use the famous MNIST data set (pre-processed via PCA and normalized [TODO]) for this tutorial, so our class labels are {0, 1, …, 9}. If you're like me, you may have found this notation a little confusing at first. We can read the left side P(C X) as "the probability that the class is C given the data X". We can read the right side P(X C) as "the probability that the data X belongs to the class C". (this is called the "likelihood") And we can compute the probability that the class 0 given the data, probability that the class 1 given the data, etc. just by computing the probability of the data for each class (how well the data fits a model of each class).

Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often sampled using simulated tempering, which augments the target space with an auxiliary inverse temperature variable. Our method exploits the multinomial probability law of the inverse temperatures, and provides estimates of the partition function in terms of a simple quotient of Rao-Blackwellized marginal inverse temperature probability estimates, which are updated while sampling. We show that the method has interesting connections with several alternative popular methods, and offers some significant advantages. In particular, we empirically find that the new method provides more accurate estimates than Annealed Importance Sampling when calculating partition functions of large Restricted Boltzmann Machines (RBM); moreover, the method is sufficiently accurate to track training and validation log-likelihoods during learning of RBMs, at minimal computational cost.

In many machine learning applications, crowdsourcing has become the primary means for label collection. In this paper, we study the optimal error rate for aggregating labels provided by a set of non-expert workers. Under the classic Dawid-Skene model, we establish matching upper and lower bounds with an exact exponent $mI(\pi)$ in which $m$ is the number of workers and $I(\pi)$ the average Chernoff information that characterizes the workers' collective ability. Such an exact characterization of the error exponent allows us to state a precise sample size requirement $m>\frac{1}{I(\pi)}\log\frac{1}{\epsilon}$ in order to achieve an $\epsilon$ misclassification error. In addition, our results imply the optimality of various EM algorithms for crowdsourcing initialized by consistent estimators.

We show that a neural network with arbitrary depth and non-linearities, with dropout applied before every weight layer, is mathematically equivalent to an approximation to a well known Bayesian model. This interpretation might offer an explanation to some of dropout's key properties, such as its robustness to over-fitting. Our interpretation allows us to reason about uncertainty in deep learning, and allows the introduction of the Bayesian machinery into existing deep learning frameworks in a principled way. This document is an appendix for the main paper "Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning" by Gal and Ghahramani, 2015.

A Markov chain is a random process with the property that the next state depends only on the current state. For example: If you have the choice of red or blue twice the process would be Markovian if each time you chose the decision had nothing to do with your choice previously (see diagram below). How can Markov Chains help us? To start with we need to define some basic terminology. The changes of state within the system are called transitions, and the probabilities associated with various state-changes are called transition probabilities.