Hyperparameter optimization for machine learning models is typically carried out by some sort of cross-validation procedure or global optimization, both of which require running the learning algorithm numerous times. We show that for Bayesian hierarchical models there is an appealing alternative that allows selecting good hyperparameters without learning the model parameters during the process at all, facilitated by the prior predictive distribution that marginalizes out the model parameters. We propose an approach that matches suitable statistics of the prior predictive distribution with ones provided by an expert and apply the general concept for matrix factorization models. For some Poisson matrix factorization models we can analytically obtain exact hyperparameters, including the number of factors, and for more complex models we propose a model-independent optimization procedure.

Editor's note: James is a speaker for ODSC London this November! Be sure to check out his talk, "The How, Why, and When of Replacing Engineering Work with Compute Power" there. Deep learning has been made practical through modern computing power, but it is not the only technique benefiting from this large increase in power. Bayesian inference is up and coming technique whose recent progress is powered by the increase in computing power. We can explain the mathematical expression of Bayes formula using an example similar to the great Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference to a financial context and using mathematical concepts intuitively arise from code.

Cross-entropy is commonly used in machine learning as a loss function. Cross-entropy is a measure from the field of information theory, building upon entropy and generally calculating the difference between two probability distributions. It is closely related to but is different from KL divergence that calculates the relative entropy between two probability distributions, whereas cross-entropy can be thought to calculate the total entropy between the distributions. Cross-entropy is also related to and often confused with logistic loss, called log loss. Although the two measures are derived from a different source, when used as loss functions for classification models, both measures calculate the same quantity and can be used interchangeably. In this tutorial, you will discover cross-entropy for machine learning.

Cross-entropy is commonly used in machine learning as a loss function. Cross-entropy is a measure from the field of information theory, building upon entropy and generally calculating the difference between two probability distributions. It is closely related to but is different from KL divergence that calculates the relative entropy between two probability distributions, whereas cross-entropy can be thought to calculate the total entropy between the distributions. Cross-entropy is also related to and often confused with logistic loss, called log loss. Although the two measures are derived from a different source, when used as loss functions for classification models, both measures calculate the same quantity and can be used interchangeably. In this tutorial, you will discover cross-entropy for machine learning.

Density estimation is the problem of estimating the probability distribution for a sample of observations from a problem domain. There are many techniques for solving density estimation, although a common framework used throughout the field of machine learning is maximum likelihood estimation. Maximum likelihood estimation involves defining a likelihood function for calculating the conditional probability of observing the data sample given a probability distribution and distribution parameters. This approach can be used to search a space of possible distributions and parameters. This flexible probabilistic framework also provides the foundation for many machine learning algorithms, including important methods such as linear regression and logistic regression for predicting numeric values and class labels respectively, but also more generally for deep learning artificial neural networks.

Real-world datasets are often biased with respect to key demographic factors such as race and gender. Due to the latent nature of the underlying factors, detecting and mitigating bias is especially challenging for unsupervised machine learning. We present a weakly supervised algorithm for overcoming dataset bias for deep generative models. Our approach requires access to an additional small, unlabeled but unbiased dataset as the supervision signal, thus sidestepping the need for explicit labels on the underlying bias factors. Using this supplementary dataset, we detect the bias in existing datasets via a density ratio technique and learn generative models which efficiently achieve the twin goals of: 1) data efficiency by using training examples from both biased and unbiased datasets for learning, 2) unbiased data generation at test time. Empirically, we demonstrate the efficacy of our approach which reduces bias w.r.t. latent factors by 57.1% on average over baselines for comparable image generation using generative adversarial networks.

Developing electrophysiological recordings of brain neuronal activity and their analysis provide a basis for exploring the structure of brain function and nervous system investigation. The recorded signals are typically a combination of spikes and noise. High amounts of background noise and possibility of electric signaling recording from several neurons adjacent to the recording site have led scientists to develop neuronal signal processing tools such as spike sorting to facilitate brain data analysis. Spike sorting plays a pivotal role in understanding the electrophysiological activity of neuronal networks. This process prepares recorded data for interpretations of neurons interactions and understanding the overall structure of brain functions. Spike sorting consists of three steps: spike detection, feature extraction, and spike clustering. There are several methods to implement each of spike sorting steps. This paper provides a systematic comparison of various spike sorting sub-techniques applied to real extracellularly recorded data from a rat brain basolateral amygdala. An efficient sorted data resulted from careful choice of spike sorting sub-methods leads to better interpretation of the brain structures connectivity under different conditions, which is a very sensitive concept in diagnosis and treatment of neurological disorders. Here, spike detection is performed by appropriate choice of threshold level via three different approaches. Feature extraction is done through PCA and Kernel PCA methods, which Kernel PCA outperforms. We have applied four different algorithms for spike clustering including K-means, Fuzzy C-means, Bayesian and Fuzzy maximum likelihood estimation. As one requirement of most clustering algorithms, optimal number of clusters is achieved through validity indices for each method. Finally, the sorting results are evaluated using inter-spike interval histograms.

Graph convolutional neural networks (GCNN) have been successfully applied to many different graph based learning tasks including node and graph classification, matrix completion, and learning of node embeddings. Despite their impressive performance, the techniques have a limited capability to incorporate the uncertainty in the underlined graph structure. In order to address this issue, a Bayesian GCNN (BGCN) framework was recently proposed. In this framework, the observed graph is considered to be a random realization from a parametric random graph model and the joint Bayesian inference of the graph and GCNN weights is performed. In this paper, we propose a non-parametric generative model for graphs and incorporate it within the BGCN framework. In addition to the observed graph, our approach effectively uses the node features and training labels in the posterior inference of graphs and attains superior or comparable performance in benchmark node classification tasks.

The holy grail in deep neural network research is porting the memory- and computation-intensive network models on embedded platforms with a minimal compromise in model accuracy. To this end, we propose a novel approach, termed as Variational Student, where we reap the benefits of compressibility of the knowledge distillation (KD) framework, and sparsity inducing abilities of variational inference (VI) techniques. Essentially, we build a sparse student network, whose sparsity is induced by the variational parameters found via optimizing a loss function based on VI, leveraging the knowledge learnt by an accurate but complex pre-trained teacher network. Further, for sparsity enhancement, we also employ a Block Sparse Regularizer on a concatenated tensor of teacher and student network weights. We demonstrate that the marriage of KD and the VI techniques inherits compression properties from the KD framework, and enhances levels of sparsity from the VI approach, with minimal compromise in the model accuracy. We benchmark our results on LeNet MLP and VGGNet (CNN) and illustrate a memory footprint reduction of 64x and 213x on these MLP and CNN variants, respectively, without a need to retrain the teacher network. Furthermore, in the low data regime, we observed that our method outperforms state-of-the-art Bayesian techniques in terms of accuracy.

A multi-layer deep Gaussian process (DGP) model is a hierarchical composition of GP models with a greater expressive power. Exact DGP inference is intractable, which has motivated the recent development of deterministic and stochastic approximation methods. Unfortunately, the deterministic approximation methods yield a biased posterior belief while the stochastic one is computationally costly. This paper presents an implicit posterior variational inference (IPVI) framework for DGPs that can ideally recover an unbiased posterior belief and still preserve time efficiency. Inspired by generative adversarial networks, our IPVI framework achieves this by casting the DGP inference problem as a two-player game in which a Nash equilibrium, interestingly, coincides with an unbiased posterior belief. This consequently inspires us to devise a best-response dynamics algorithm to search for a Nash equilibrium (i.e., an unbiased posterior belief). Empirical evaluation shows that IPVI outperforms the state-of-the-art approximation methods for DGPs.