Estimating Cosmological Parameters from the Dark Matter Distribution

A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe. Galaxy surveys provide the means to map out cosmic large-scale structure in three dimensions. Information about galaxy locations is typically summarized in a "single" function of scale, such as the galaxy correlation function or power-spectrum. We show that it is possible to estimate these cosmological parameters directly from the distribution of matter. This paper presents the application of deep 3D convolutional networks to volumetric representation of dark-matter simulations as well as the results obtained using a recently proposed distribution regression framework, showing that machine learning techniques are comparable to, and can sometimes outperform, maximum-likelihood point estimates using "cosmological models". This opens the way to estimating the parameters of our Universe with higher accuracy.

Scaling Active Search using Linear Similarity Functions

Active Search has become an increasingly useful tool in information retrieval problems where the goal is to discover as many target elements as possible using only limited label queries. With the advent of big data, there is a growing emphasis on the scalability of such techniques to handle very large and very complex datasets. In this paper, we consider the problem of Active Search where we are given a similarity function between data points. We look at an algorithm introduced by Wang et al. [2013] for Active Search over graphs and propose crucial modifications which allow it to scale significantly. Their approach selects points by minimizing an energy function over the graph induced by the similarity function on the data. Our modifications require the similarity function to be a dot-product between feature vectors of data points, equivalent to having a linear kernel for the adjacency matrix. With this, we are able to scale tremendously: for $n$ data points, the original algorithm runs in $O(n^2)$ time per iteration while ours runs in only $O(nr + r^2)$ given $r$-dimensional features. We also describe a simple alternate approach using a weighted-neighbor predictor which also scales well. In our experiments, we show that our method is competitive with existing semi-supervised approaches. We also briefly discuss conditions under which our algorithm performs well.

Equivariance Through Parameter-Sharing

We propose to study equivariance in deep neural networks through parameter symmetries. In particular, given a group $\mathcal{G}$ that acts discretely on the input and output of a standard neural network layer $\phi_{W}: \Re^{M} \to \Re^{N}$, we show that $\phi_{W}$ is equivariant with respect to $\mathcal{G}$-action iff $\mathcal{G}$ explains the symmetries of the network parameters $W$. Inspired by this observation, we then propose two parameter-sharing schemes to induce the desirable symmetry on $W$. Our procedures for tying the parameters achieve $\mathcal{G}$-equivariance and, under some conditions on the action of $\mathcal{G}$, they guarantee sensitivity to all other permutation groups outside $\mathcal{G}$.

Recurrent Estimation of Distributions

This paper presents the recurrent estimation of distributions (RED) for modeling real-valued data in a semiparametric fashion. RED models make two novel uses of recurrent neural networks (RNNs) for density estimation of general real-valued data. First, RNNs are used to transform input covariates into a latent space to better capture conditional dependencies in inputs. After, an RNN is used to compute the conditional distributions of the latent covariates. The resulting model is efficient to train, compute, and sample from, whilst producing normalized pdfs. The effectiveness of RED is shown via several real-world data experiments. Our results show that RED models achieve a lower held-out negative log-likelihood than other neural network approaches across multiple dataset sizes and dimensionalities. Further context of the efficacy of RED is provided by considering anomaly detection tasks, where we also observe better performance over alternative models.

Asynchronous Parallel Bayesian Optimisation via Thompson Sampling

We design and analyse variations of the classical Thompson sampling (TS) procedure for Bayesian optimisation (BO) in settings where function evaluations are expensive, but can be performed in parallel. Our theoretical analysis shows that a direct application of the sequential Thompson sampling algorithm in either synchronous or asynchronous parallel settings yields a surprisingly powerful result: making $n$ evaluations distributed among $M$ workers is essentially equivalent to performing $n$ evaluations in sequence. Further, by modeling the time taken to complete a function evaluation, we show that, under a time constraint, asynchronously parallel TS achieves asymptotically lower regret than both the synchronous and sequential versions. These results are complemented by an experimental analysis, showing that asynchronous TS outperforms a suite of existing parallel BO algorithms in simulations and in a hyper-parameter tuning application in convolutional neural networks. In addition to these, the proposed procedure is conceptually and computationally much simpler than existing work for parallel BO.

Multi-fidelity Bayesian Optimisation with Continuous Approximations

Bandit methods for black-box optimisation, such as Bayesian optimisation, are used in a variety of applications including hyper-parameter tuning and experiment design. Recently, \emph{multi-fidelity} methods have garnered considerable attention since function evaluations have become increasingly expensive in such applications. Multi-fidelity methods use cheap approximations to the function of interest to speed up the overall optimisation process. However, most multi-fidelity methods assume only a finite number of approximations. In many practical applications however, a continuous spectrum of approximations might be available. For instance, when tuning an expensive neural network, one might choose to approximate the cross validation performance using less data $N$ and/or few training iterations $T$. Here, the approximations are best viewed as arising out of a continuous two dimensional space $(N,T)$. In this work, we develop a Bayesian optimisation method, BOCA, for this setting. We characterise its theoretical properties and show that it achieves better regret than than strategies which ignore the approximations. BOCA outperforms several other baselines in synthetic and real experiments.

The Statistical Recurrent Unit

Sophisticated gated recurrent neural network architectures like LSTMs and GRUs have been shown to be highly effective in a myriad of applications. We develop an un-gated unit, the statistical recurrent unit (SRU), that is able to learn long term dependencies in data by only keeping moving averages of statistics. The SRU's architecture is simple, un-gated, and contains a comparable number of parameters to LSTMs; yet, SRUs perform favorably to more sophisticated LSTM and GRU alternatives, often outperforming one or both in various tasks. We show the efficacy of SRUs as compared to LSTMs and GRUs in an unbiased manner by optimizing respective architectures' hyperparameters in a Bayesian optimization scheme for both synthetic and real-world tasks.

Deep Learning with Sets and Point Clouds

We introduce a simple permutation equivariant layer for deep learning with set structure.This type of layer, obtained by parameter-sharing, has a simple implementation and linear-time complexity in the size of each set. We use deep permutation-invariant networks to perform point-could classification and MNIST-digit summation, where in both cases the output is invariant to permutations of the input. In a semi-supervised setting, where the goal is make predictions for each instance within a set, we demonstrate the usefulness of this type of layer in set-outlier detection as well as semi-supervised learning with clustering side-information.

Query Efficient Posterior Estimation in Scientific Experiments via Bayesian Active Learning

A common problem in disciplines of applied Statistics research such as Astrostatistics is of estimating the posterior distribution of relevant parameters. Typically, the likelihoods for such models are computed via expensive experiments such as cosmological simulations of the universe. An urgent challenge in these research domains is to develop methods that can estimate the posterior with few likelihood evaluations. In this paper, we study active posterior estimation in a Bayesian setting when the likelihood is expensive to evaluate. Existing techniques for posterior estimation are based on generating samples representative of the posterior. Such methods do not consider efficiency in terms of likelihood evaluations. In order to be query efficient we treat posterior estimation in an active regression framework. We propose two myopic query strategies to choose where to evaluate the likelihood and implement them using Gaussian processes. Via experiments on a series of synthetic and real examples we demonstrate that our approach is significantly more query efficient than existing techniques and other heuristics for posterior estimation.

Active Search for Sparse Signals with Region Sensing

Autonomous systems can be used to search for sparse signals in a large space; e.g., aerial robots can be deployed to localize threats, detect gas leaks, or respond to distress calls. Intuitively, search algorithms may increase efficiency by collecting aggregate measurements summarizing large contiguous regions. However, most existing search methods either ignore the possibility of such region observations (e.g., Bayesian optimization and multi-armed bandits) or make strong assumptions about the sensing mechanism that allow each measurement to arbitrarily encode all signals in the entire environment (e.g., compressive sensing). We propose an algorithm that actively collects data to search for sparse signals using only noisy measurements of the average values on rectangular regions (including single points), based on the greedy maximization of information gain. We analyze our algorithm in 1d and show that it requires $\tilde{O}(\frac{n}{\mu^2}+k^2)$ measurements to recover all of $k$ signal locations with small Bayes error, where $\mu$ and $n$ are the signal strength and the size of the search space, respectively. We also show that active designs can be fundamentally more efficient than passive designs with region sensing, contrasting with the results of Arias-Castro, Candes, and Davenport (2013). We demonstrate the empirical performance of our algorithm on a search problem using satellite image data and in high dimensions.