A Unified Approach for Learning the Parameters of Sum-Product Networks

We present a unified approach for learning the parameters of Sum-Product networks (SPNs). We prove that any complete and decomposable SPN is equivalent to a mixture of trees where each tree corresponds to a product of univariate distributions. Based on the mixture model perspective, we characterize the objective function when learning SPNs based on the maximum likelihood estimation (MLE) principle and show that the optimization problem can be formulated as a signomial program. We construct two parameter learning algorithms for SPNs by using sequential monomial approximations (SMA) and the concave-convex procedure (CCCP), respectively. The two proposed methods naturally admit multiplicative updates, hence effectively avoiding the projection operation. With the help of the unified framework, we also show that, in the case of SPNs, CCCP leads to the same algorithm as Expectation Maximization (EM) despite the fact that they are different in general.Comment: NIPS 201

Sum-of-Squares Polynomial Flow

Triangular map is a recent construct in probability theory that allows one to transform any source probability density function to any target density function. Based on triangular maps, we propose a general framework for high-dimensional density estimation, by specifying one-dimensional transformations (equivalently conditional densities) and appropriate conditioner networks. This framework (a) reveals the commonalities and differences of existing autoregressive and flow based methods, (b) allows a unified understanding of the limitations and representation power of these recent approaches and, (c) motivates us to uncover a new Sum-of-Squares (SOS) flow that is interpretable, universal, and easy to train. We perform several synthetic experiments on various density geometries to demonstrate the benefits (and short-comings) of such transformations. SOS flows achieve competitive results in simulations and several real-world datasets.Comment: 13 pages, ICML'201

Deep Compression of Sum-Product Networks on Tensor Networks

Sum-product networks (SPNs) represent an emerging class of neural networks with clear probabilistic semantics and superior inference speed over graphical models. This work reveals a strikingly intimate connection between SPNs and tensor networks, thus leading to a highly efficient representation that we call tensor SPNs (tSPNs). For the first time, through mapping an SPN onto a tSPN and employing novel optimization techniques, we demonstrate remarkable parameter compression with negligible loss in accuracy

From Pixels to Buildings: End-to-end Probabilistic Deep Networks for Large-scale Semantic Mapping

We introduce TopoNets, end-to-end probabilistic deep networks for modeling semantic maps with structure reflecting the topology of large-scale environments. TopoNets build a unified deep network spanning multiple levels of abstraction and spatial scales, from pixels representing geometry of local places to high-level descriptions of semantics of buildings. To this end, TopoNets leverage complex spatial relations expressed in terms of arbitrary, dynamic graphs. We demonstrate how TopoNets can be used to perform end-to-end semantic mapping from partial sensory observations and noisy topological relations discovered by a robot exploring large-scale office spaces. Thanks to their probabilistic nature and generative properties, TopoNets extend the problem of semantic mapping beyond classification. We show that TopoNets successfully perform uncertain reasoning about yet unexplored space and detect novel and incongruent environment configurations unknown to the robot. Our implementation of TopoNets achieves real-time, tractable and exact inference, which makes these new deep models a promising, practical solution to mobile robot spatial understanding at scale.Comment: 8 pages, 8 figures, 1 table. The 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2019

Data-Dependent Path Normalization in Neural Networks

We propose a unified framework for neural net normalization, regularization and optimization, which includes Path-SGD and Batch-Normalization and interpolates between them across two different dimensions. Through this framework we investigate issue of invariance of the optimization, data dependence and the connection with natural gradients.Comment: 17 pages, 3 figure

Stochastic And-Or Grammars: A Unified Framework and Logic Perspective

Stochastic And-Or grammars (AOG) extend traditional stochastic grammars of language to model other types of data such as images and events. In this paper we propose a representation framework of stochastic AOGs that is agnostic to the type of the data being modeled and thus unifies various domain-specific AOGs. Many existing grammar formalisms and probabilistic models in natural language processing, computer vision, and machine learning can be seen as special cases of this framework. We also propose a domain-independent inference algorithm of stochastic context-free AOGs and show its tractability under a reasonable assumption. Furthermore, we provide two interpretations of stochastic context-free AOGs as a subset of probabilistic logic, which connects stochastic AOGs to the field of statistical relational learning and clarifies their relation with a few existing statistical relational models

Alternating Diffusion Map Based Fusion of Multimodal Brain Connectivity Networks for IQ Prediction

To explain individual differences in development, behavior, and cognition, most previous studies focused on projecting resting-state functional MRI (fMRI) based functional connectivity (FC) data into a low-dimensional space via linear dimensionality reduction techniques, followed by executing analysis operations. However, linear dimensionality analysis techniques may fail to capture nonlinearity of brain neuroactivity. Moreover, besides resting-state FC, FC based on task fMRI can be expected to provide complementary information. Motivated by these considerations, we nonlinearly fuse resting-state and task-based FC networks (FCNs) to seek a better representation in this paper. We propose a framework based on alternating diffusion map (ADM), which extracts geometry-preserving low-dimensional embeddings that successfully parameterize the intrinsic variables driving the phenomenon of interest. Specifically, we first separately build resting-state and task-based FCNs by symmetric positive definite matrices using sparse inverse covariance estimation for each subject, and then utilize the ADM to fuse them in order to extract significant low-dimensional embeddings, which are used as fingerprints to identify individuals. The proposed framework is validated on the Philadelphia Neurodevelopmental Cohort data, where we conduct extensive experimental study on resting-state and fractal $n$-back task fMRI for the classification of intelligence quotient (IQ). The fusion of resting-state and $n$-back task fMRI by the proposed framework achieves better classification accuracy than any single fMRI, and the proposed framework is shown to outperform several other data fusion methods. To our knowledge, this paper is the first to demonstrate a successful extension of the ADM to fuse resting-state and task-based fMRI data for accurate prediction of IQ

Dynamic Few-Shot Visual Learning without Forgetting

The human visual system has the remarkably ability to be able to effortlessly learn novel concepts from only a few examples. Mimicking the same behavior on machine learning vision systems is an interesting and very challenging research problem with many practical advantages on real world vision applications. In this context, the goal of our work is to devise a few-shot visual learning system that during test time it will be able to efficiently learn novel categories from only a few training data while at the same time it will not forget the initial categories on which it was trained (here called base categories). To achieve that goal we propose (a) to extend an object recognition system with an attention based few-shot classification weight generator, and (b) to redesign the classifier of a ConvNet model as the cosine similarity function between feature representations and classification weight vectors. The latter, apart from unifying the recognition of both novel and base categories, it also leads to feature representations that generalize better on "unseen" categories. We extensively evaluate our approach on Mini-ImageNet where we manage to improve the prior state-of-the-art on few-shot recognition (i.e., we achieve 56.20% and 73.00% on the 1-shot and 5-shot settings respectively) while at the same time we do not sacrifice any accuracy on the base categories, which is a characteristic that most prior approaches lack. Finally, we apply our approach on the recently introduced few-shot benchmark of Bharath and Girshick [4] where we also achieve state-of-the-art results. The code and models of our paper will be published on: https://github.com/gidariss/FewShotWithoutForgettingComment: Accepted at CVPR 2018. Code and models will be published on: https://github.com/gidariss/FewShotWithoutForgettin

A Connection between Feed-Forward Neural Networks and Probabilistic Graphical Models

Two of the most popular modelling paradigms in computer vision are feed-forward neural networks (FFNs) and probabilistic graphical models (GMs). Various connections between the two have been studied in recent works, such as e.g. expressing mean-field based inference in a GM as an FFN. This paper establishes a new connection between FFNs and GMs. Our key observation is that any FFN implements a certain approximation of a corresponding Bayesian network (BN). We characterize various benefits of having this connection. In particular, it results in a new learning algorithm for BNs. We validate the proposed methods for a classification problem on CIFAR-10 dataset and for binary image segmentation on Weizmann Horse dataset. We show that statistically learned BNs improve performance, having at the same time essentially better generalization capability, than their FFN counterparts

Learning Large-Scale Topological Maps Using Sum-Product Networks

In order to perform complex actions in human environments, an autonomous robot needs the ability to understand the environment, that is, to gather and maintain spatial knowledge. Topological map is commonly used for representing large scale, global maps such as floor plans. Although much work has been done in topological map extraction, we have found little previous work on the problem of learning the topological map using a probabilistic model. Learning a topological map means learning the structure of the large-scale space and dependency between places, for example, how the evidence of a group of places influence the attributes of other places. This is an important step towards planning complex actions in the environment. In this thesis, we consider the problem of using probabilistic deep learning model to learn the topological map, which is essentially a sparse undirected graph where nodes represent places annotated with their semantic attributes (e.g. place category). We propose to use a novel probabilistic deep model, Sum-Product Networks (SPNs), due to their unique properties. We present two methods for learning topological maps using SPNs: the place grid method and the template-based method. We contribute an algorithm that builds SPNs for graphs using template models. Our experiments evaluate the ability of our models to enable robots to infer semantic attributes and detect maps with novel semantic attribute arrangements. Our results demonstrate their understanding of the topological map structure and spatial relations between places.Comment: 26 pages, 14 figures, senior thesis for departmental honors at the Allen School of Computer Science and Engineering at the University of Washingto