Passing Expectation Propagation Messages with Kernel Methods

We propose to learn a kernel-based message operator which takes as input all expectation propagation (EP) incoming messages to a factor node and produces an outgoing message. In ordinary EP, computing an outgoing message involves estimating a multivariate integral which may not have an analytic expression. Learning such an operator allows one to bypass the expensive computation of the integral during inference by directly mapping all incoming messages into an outgoing message. The operator can be learned from training data (examples of input and output messages) which allows automated inference to be made on any kind of factor that can be sampled.Comment: Accepted to Advances in Variational Inference, NIPS 2014 Worksho

On Deep Set Learning and the Choice of Aggregations

Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep Set learning. This work investigates a core component of Deep Set architecture: aggregation functions. We suggest and examine alternatives to commonly used aggregation functions, including learnable recurrent aggregation functions. Empirically, we show that the Deep Set networks are highly sensitive to the choice of aggregation functions: beyond improved performance, we find that learnable aggregations lower hyper-parameter sensitivity and generalize better to out-of-distribution input size

Dataset2Vec: Learning Dataset Meta-Features

Meta-learning, or learning to learn, is a machine learning approach that utilizes prior learning experiences to expedite the learning process on unseen tasks. As a data-driven approach, meta-learning requires meta-features that represent the primary learning tasks or datasets, and are estimated traditonally as engineered dataset statistics that require expert domain knowledge tailored for every meta-task. In this paper, first, we propose a meta-feature extractor called Dataset2Vec that combines the versatility of engineered dataset meta-features with the expressivity of meta-features learned by deep neural networks. Primary learning tasks or datasets are represented as hierarchical sets, i.e., as a set of sets, esp. as a set of predictor/target pairs, and then a DeepSet architecture is employed to regress meta-features on them. Second, we propose a novel auxiliary meta-learning task with abundant data called dataset similarity learning that aims to predict if two batches stem from the same dataset or different ones. In an experiment on a large-scale hyperparameter optimization task for 120 UCI datasets with varying schemas as a meta-learning task, we show that the meta-features of Dataset2Vec outperform the expert engineered meta-features and thus demonstrate the usefulness of learned meta-features for datasets with varying schemas for the first time

On The Identifiability of Mixture Models from Grouped Samples

Finite mixture models are statistical models which appear in many problems in statistics and machine learning. In such models it is assumed that data are drawn from random probability measures, called mixture components, which are themselves drawn from a probability measure P over probability measures. When estimating mixture models, it is common to make assumptions on the mixture components, such as parametric assumptions. In this paper, we make no assumption on the mixture components, and instead assume that observations from the mixture model are grouped, such that observations in the same group are known to be drawn from the same component. We show that any mixture of m probability measures can be uniquely identified provided there are 2m-1 observations per group. Moreover we show that, for any m, there exists a mixture of m probability measures that cannot be uniquely identified when groups have 2m-2 observations. Our results hold for any sample space with more than one element

Linear-time Learning on Distributions with Approximate Kernel Embeddings

Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so through pairwise kernel evaluations between pdfs (or sample sets). While such an approach is fine for smaller datasets, the computation of an $N \times N$ Gram matrix is prohibitive in large datasets. Recent scalable estimators that work over pdfs have done so only with kernels that use Euclidean metrics, like the $L_2$ distance. However, there are a myriad of other useful metrics available, such as total variation, Hellinger distance, and the Jensen-Shannon divergence. This work develops the first random features for pdfs whose dot product approximates kernels using these non-Euclidean metrics, allowing estimators using such kernels to scale to large datasets by working in a primal space, without computing large Gram matrices. We provide an analysis of the approximation error in using our proposed random features and show empirically the quality of our approximation both in estimating a Gram matrix and in solving learning tasks in real-world and synthetic data

3D Object Recognition with Ensemble Learning --- A Study of Point Cloud-Based Deep Learning Models

In this study, we present an analysis of model-based ensemble learning for 3D point-cloud object classification and detection. An ensemble of multiple model instances is known to outperform a single model instance, but there is little study of the topic of ensemble learning for 3D point clouds. First, an ensemble of multiple model instances trained on the same part of the $\textit{ModelNet40}$ dataset was tested for seven deep learning, point cloud-based classification algorithms: $\textit{PointNet}$, $\textit{PointNet++}$, $\textit{SO-Net}$, $\textit{KCNet}$, $\textit{DeepSets}$, $\textit{DGCNN}$, and $\textit{PointCNN}$. Second, the ensemble of different architectures was tested. Results of our experiments show that the tested ensemble learning methods improve over state-of-the-art on the $\textit{ModelNet40}$ dataset, from $92.65\%$ to $93.64\%$ for the ensemble of single architecture instances, $94.03\%$ for two different architectures, and $94.15\%$ for five different architectures. We show that the ensemble of two models with different architectures can be as effective as the ensemble of 10 models with the same architecture. Third, a study on classic bagging i.e. with different subsets used for training multiple model instances) was tested and sources of ensemble accuracy growth were investigated for best-performing architecture, i.e. $\textit{SO-Net}$. We also investigate the ensemble learning of $\textit{Frustum PointNet}$ approach in the task of 3D object detection, increasing the average precision of 3D box detection on the $\textit{KITTI}$ dataset from $63.1\%$ to $66.5\%$ using only three model instances. We measure the inference time of all 3D classification architectures on a $\textit{Nvidia Jetson TX2}$, a common embedded computer for mobile robots, to allude to the use of these models in real-life applications

FuSSO: Functional Shrinkage and Selection Operator

We present the FuSSO, a functional analogue to the LASSO, that efficiently finds a sparse set of functional input covariates to regress a real-valued response against. The FuSSO does so in a semi-parametric fashion, making no parametric assumptions about the nature of input functional covariates and assuming a linear form to the mapping of functional covariates to the response. We provide a statistical backing for use of the FuSSO via proof of asymptotic sparsistency under various conditions. Furthermore, we observe good results on both synthetic and real-world data

Causal effects based on distributional distances

We develop a novel framework for estimating causal effects based on the discrepancy between unobserved counterfactual distributions. In our setting a causal effect is defined in terms of the $L_1$ distance between different counterfactual outcome distributions, rather than a mean difference in outcome values. Directly comparing counterfactual outcome distributions can provide more nuanced and valuable information about causality than a simple comparison of means. We consider single- and multi-source randomized studies, as well as observational studies, and analyze error bounds and asymptotic properties of the proposed estimators. We further propose methods to construct confidence intervals for the unknown mean distribution distance. Finally, we illustrate the new methods and verify their effectiveness in empirical studies.Comment: 31 page

Causal inference using deep neural networks

Causal inference from observation data is a core problem in many scientific fields. Here we present a general supervised deep learning framework that infers causal interactions by transforming the input vectors to an image-like representation for every pair of inputs. Given a training dataset we first construct a normalized empirical probability density distribution (NEPDF) matrix. We then train a convolutional neural network (CNN) on NEPDFs for causality predictions. We tested the method on several different simulated and real world data and compared it to prior methods for causal inference. As we show, the method is general, can efficiently handle very large datasets and improves upon prior methods

Kernel Mean Embedding of Distributions: A Review and Beyond

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing kernel Hilbert space (RKHS) in which the whole arsenal of kernel methods can be extended to probability measures. It can be viewed as a generalization of the original "feature map" common to support vector machines (SVMs) and other kernel methods. While initially closely associated with the latter, it has meanwhile found application in fields ranging from kernel machines and probabilistic modeling to statistical inference, causal discovery, and deep learning. The goal of this survey is to give a comprehensive review of existing work and recent advances in this research area, and to discuss the most challenging issues and open problems that could lead to new research directions. The survey begins with a brief introduction to the RKHS and positive definite kernels which forms the backbone of this survey, followed by a thorough discussion of the Hilbert space embedding of marginal distributions, theoretical guarantees, and a review of its applications. The embedding of distributions enables us to apply RKHS methods to probability measures which prompts a wide range of applications such as kernel two-sample testing, independent testing, and learning on distributional data. Next, we discuss the Hilbert space embedding for conditional distributions, give theoretical insights, and review some applications. The conditional mean embedding enables us to perform sum, product, and Bayes' rules---which are ubiquitous in graphical model, probabilistic inference, and reinforcement learning---in a non-parametric way. We then discuss relationships between this framework and other related areas. Lastly, we give some suggestions on future research directions.Comment: 147 pages; this is a version of the manuscript after the review proces