Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing link" between independent Monte Carlo sampling and deterministic evaluation on regular grids, applicable to a general set of spaces. This is helpful whenever an algorithm *explores* to reduce uncertainty, such as in active learning, Bayesian optimization, reinforcement learning, and marginalization in graphical models. To draw samples from a DPP in practice, existing literature focuses on approximate schemes of low cost, or comparably inefficient exact algorithms like rejection sampling. We point out that, for many settings of relevance to machine learning, it is also possible to draw *exact* samples from DPPs on continuous domains. We start from an intuitive example on the real line, which is then generalized to multivariate real vector spaces. We also compare to previously studied approximations, showing that exact sampling, despite higher cost, can be preferable where precision is needed.

We describe our experience in the development of a probabilistic network for the diagnosis of acute cardiopulmonary diseases. A panel of expert physicians collaborated to specify the qualitative part, that is a directed acyclic graph defining a factorization of the joint probability distribution of domain variables. The quantitative part, that is the set of all conditional probability distributions defined by each factor, was estimated in the Bayesian paradigm: we applied a special formal representation, characterized by a low number of parameters and a parameterization intelligible for physicians, elicited the joint prior distribution of parameters from medical experts, and updated it by conditioning on a dataset of hospital patient records using Markov Chain Monte Carlo simulation. Refinement was cyclically performed until the probabilistic network provided satisfactory Concordance Index values for a selection of acute diseases and reasonable inference on six fictitious patient cases. The probabilistic network can be employed to perform medical diagnosis on a total of 63 diseases (38 acute and 25 chronic) on the basis of up to 167 patient findings.

When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special case of regularized M-estimation, as a surrogate. However, MAP is suboptimal in high dimensions, when the number of unknown signal components is similar to the number of measurements. In this work we demonstrate, when the signal distribution and the likelihood function associated with the noise are both log-concave, that optimal MMSE performance is asymptotically achievable via another M-estimation procedure. This procedure involves minimizing convex loss and regularizer functions that are nonlinearly smoothed versions of the widely applied MAP optimization problem. Our findings provide a new heuristic derivation and interpretation for recent optimal M-estimators found in the setting of linear measurements and additive noise, and further extend these results to nonlinear measurements with non-additive noise. We numerically demonstrate superior performance of our optimal M-estimators relative to MAP. Overall, at the heart of our work is the revelation of a remarkable equivalence between two seemingly very different computational problems: namely that of high dimensional Bayesian integration underlying MMSE inference, and high dimensional convex optimization underlying M-estimation. In essence we show that the former difficult integral may be computed by solving the latter, simpler optimization problem.

We introduce Delay Pruning, a simple yet powerful technique to regularize dynamic Boltzmann machines (DyBM). The recently introduced DyBM provides a particularly structured Boltzmann machine, as a generative model of a multi-dimensional time-series. This Boltzmann machine can have infinitely many layers of units but allows exact inference and learning based on its biologically motivated structure. DyBM uses the idea of conduction delays in the form of fixed length first-in first-out (FIFO) queues, with a neuron connected to another via this FIFO queue, and spikes from a pre-synaptic neuron travel along the queue to the post-synaptic neuron with a constant period of delay. Here, we present Delay Pruning as a mechanism to prune the lengths of the FIFO queues (making them zero) by setting some delay lengths to one with a fixed probability, and finally selecting the best performing model with fixed delays. The uniqueness of structure and a non-sampling based learning rule in DyBM, make the application of previously proposed regularization techniques like Dropout or DropConnect difficult, leading to poor generalization. First, we evaluate the performance of Delay Pruning to let DyBM learn a multidimensional temporal sequence generated by a Markov chain. Finally, we show the effectiveness of delay pruning in learning high dimensional sequences using the moving MNIST dataset, and compare it with Dropout and DropConnect methods.

Bibliographic analysis considers the author's research areas, the citation network and the paper content among other things. In this paper, we combine these three in a topic model that produces a bibliographic model of authors, topics and documents, using a nonparametric extension of a combination of the Poisson mixed-topic link model and the author-topic model. This gives rise to the Citation Network Topic Model (CNTM). We propose a novel and efficient inference algorithm for the CNTM to explore subsets of research publications from CiteSeerX. The publication datasets are organised into three corpora, totalling to about 168k publications with about 62k authors. The queried datasets are made available online. In three publicly available corpora in addition to the queried datasets, our proposed model demonstrates an improved performance in both model fitting and document clustering, compared to several baselines. Moreover, our model allows extraction of additional useful knowledge from the corpora, such as the visualisation of the author-topics network. Additionally, we propose a simple method to incorporate supervision into topic modelling to achieve further improvement on the clustering task.

The Dirichlet process and its extension, the Pitman-Yor process, are stochastic processes that take probability distributions as a parameter. These processes can be stacked up to form a hierarchical nonparametric Bayesian model. In this article, we present efficient methods for the use of these processes in this hierarchical context, and apply them to latent variable models for text analytics. In particular, we propose a general framework for designing these Bayesian models, which are called topic models in the computer science community. We then propose a specific nonparametric Bayesian topic model for modelling text from social media. We focus on tweets (posts on Twitter) in this article due to their ease of access. We find that our nonparametric model performs better than existing parametric models in both goodness of fit and real world applications.

We describe a method for parameter estimation in bipartite probabilistic graphical models for joint prediction of clinical conditions from the electronic medical record. The method does not rely on the availability of gold-standard labels, but rather uses noisy labels, called anchors, for learning. We provide a likelihood-based objective and a moments-based initialization that are effective at learning the model parameters. The learned model is evaluated in a task of assigning a heldout clinical condition to patients based on retrospective analysis of the records, and outperforms baselines which do not account for the noisiness in the labels or do not model the conditions jointly.

Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. Gaussian processes (GPs) provide a Bayesian approach to learning such problems in a kernel based framework. We develop Gaussian process models based on pseudo-likelihood to solve sequence labeling problems. The pseudo-likelihood model enables one to capture multiple dependencies among the output components of the sequence without becoming computationally intractable. We use an efficient variational Gaussian approximation method to perform inference in the proposed model. We also provide an iterative algorithm which can effectively make use of the information from the neighboring labels to perform prediction. The ability to capture multiple dependencies makes the proposed approach useful for a wide range of sequence labeling problems. Numerical experiments on some sequence labeling problems in natural language processing demonstrate the usefulness of the proposed approach.

How to increase Naive Bayes accuracy? Total size of dataset was 81. Ok so I ran the program against test data and it gave me accuracy of 21% only. Can anyone tell me why is like that? Where am I going wrong?

I am learning NB algorithm and implementing on a real dataset that contains only 80 records. Now I want to prepare training data. I want to know whether training data is made from the actual data or the actual pattern given in real data? Also, does training data means covering all cases given in real data or what?