arXiv subjects

Seungjin Choi

Publications and source records attributed to Seungjin Choi.

33 records · Page 2Linked to original sources

arXiv2020

Discrete Infomax Codes for Supervised Representation Learning

Learning compact discrete representations of data is a key task on its own or for facilitating subsequent processing of data. In this paper we present a model that produces Discrete InfoMax Codes (DIMCO); we learn a probabilistic encoder that yields k-way d-dimensional codes associated with input data. Our model's learning objective is to maximize the mutual information between codes and labels with a regularization, which enforces entries of a codeword to be as independent as possible. We show that the infomax principle also justifies previous loss functions (e.g., cross-entropy) as its special cases. Our analysis also shows that using shorter codes, as DIMCO does, reduces overfitting in the context of few-shot classification. Through experiments in various domains, we observe this implicit meta-regularization effect of DIMCO. Furthermore, we show that the codes learned by DIMCO are efficient in terms of both memory and retrieval time compared to previous methods.

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arXiv2019

Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks

Many machine learning tasks such as multiple instance learning, 3D shape recognition, and few-shot image classification are defined on sets of instances. Since solutions to such problems do not depend on the order of elements of the set, models used to address them should be permutation invariant. We present an attention-based neural network module, the Set Transformer, specifically designed to model interactions among elements in the input set. The model consists of an encoder and a decoder, both of which rely on attention mechanisms. In an effort to reduce computational complexity, we introduce an attention scheme inspired by inducing point methods from sparse Gaussian process literature. It reduces the computation time of self-attention from quadratic to linear in the number of elements in the set. We show that our model is theoretically attractive and we evaluate it on a range of tasks, demonstrating the state-of-the-art performance compared to recent methods for set-structured data.

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arXiv2019

MxML: Mixture of Meta-Learners for Few-Shot Classification

A meta-model is trained on a distribution of similar tasks such that it learns an algorithm that can quickly adapt to a novel task with only a handful of labeled examples. Most of current meta-learning methods assume that the meta-training set consists of relevant tasks sampled from a single distribution. In practice, however, a new task is often out of the task distribution, yielding a performance degradation. One way to tackle this problem is to construct an ensemble of meta-learners such that each meta-learner is trained on different task distribution. In this paper we present a method for constructing a mixture of meta-learners (MxML), where mixing parameters are determined by the weight prediction network (WPN) optimized to improve the few-shot classification performance. Experiments on various datasets demonstrate that MxML significantly outperforms state-of-the-art meta-learners, or their naive ensemble in the case of out-of-distribution as well as in-distribution tasks.

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arXiv2018

Learning to Warm-Start Bayesian Hyperparameter Optimization

Hyperparameter optimization aims to find the optimal hyperparameter configuration of a machine learning model, which provides the best performance on a validation dataset. Manual search usually leads to get stuck in a local hyperparameter configuration, and heavily depends on human intuition and experience. A simple alternative of manual search is random/grid search on a space of hyperparameters, which still undergoes extensive evaluations of validation errors in order to find its best configuration. Bayesian optimization that is a global optimization method for black-box functions is now popular for hyperparameter optimization, since it greatly reduces the number of validation error evaluations required, compared to random/grid search. Bayesian optimization generally finds the best hyperparameter configuration from random initialization without any prior knowledge. This motivates us to let Bayesian optimization start from the configurations that were successful on similar datasets, which are able to remarkably minimize the number of evaluations. In this paper, we propose deep metric learning to learn meta-features over datasets such that the similarity over them is effectively measured by Euclidean distance between their associated meta-features. To this end, we introduce a Siamese network composed of deep feature and meta-feature extractors, where deep feature extractor provides a semantic representation of each instance in a dataset and meta-feature extractor aggregates a set of deep features to encode a single representation over a dataset. Then, our learned meta-features are used to select a few datasets similar to the new dataset, so that hyperparameters in similar datasets are adopted as initializations to warm-start Bayesian hyperparameter optimization.

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arXiv2018

A Bayesian model for sparse graphs with flexible degree distribution and overlapping community structure

We consider a non-projective class of inhomogeneous random graph models with interpretable parameters and a number of interesting asymptotic properties. Using the results of Bollobás et al. [2007], we show that i) the class of models is sparse and ii) depending on the choice of the parameters, the model is either scale-free, with power-law exponent greater than 2, or with an asymptotic degree distribution which is power-law with exponential cut-off. We propose an extension of the model that can accommodate an overlapping community structure. Scalable posterior inference can be performed due to the specific choice of the link probability. We present experiments on five different real-world networks with up to 100,000 nodes and edges, showing that the model can provide a good fit to the degree distribution and recovers well the latent community structure.

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arXiv2018

Gradient-Based Meta-Learning with Learned Layerwise Metric and Subspace

Gradient-based meta-learning methods leverage gradient descent to learn the commonalities among various tasks. While previous such methods have been successful in meta-learning tasks, they resort to simple gradient descent during meta-testing. Our primary contribution is the {\em MT-net}, which enables the meta-learner to learn on each layer's activation space a subspace that the task-specific learner performs gradient descent on. Additionally, a task-specific learner of an {\em MT-net} performs gradient descent with respect to a meta-learned distance metric, which warps the activation space to be more sensitive to task identity. We demonstrate that the dimension of this learned subspace reflects the complexity of the task-specific learner's adaptation task, and also that our model is less sensitive to the choice of initial learning rates than previous gradient-based meta-learning methods. Our method achieves state-of-the-art or comparable performance on few-shot classification and regression tasks.

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arXiv2017

Bayesian inference on random simple graphs with power law degree distributions

We present a model for random simple graphs with a degree distribution that obeys a power law (i.e., is heavy-tailed). To attain this behavior, the edge probabilities in the graph are constructed from Bertoin-Fujita-Roynette-Yor (BFRY) random variables, which have been recently utilized in Bayesian statistics for the construction of power law models in several applications. Our construction readily extends to capture the structure of latent factors, similarly to stochastic blockmodels, while maintaining its power law degree distribution. The BFRY random variables are well approximated by gamma random variables in a variational Bayesian inference routine, which we apply to several network datasets for which power law degree distributions are a natural assumption. By learning the parameters of the BFRY distribution via probabilistic inference, we are able to automatically select the appropriate power law behavior from the data. In order to further scale our inference procedure, we adopt stochastic gradient ascent routines where the gradients are computed on minibatches (i.e., subsets) of the edges in the graph.

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arXiv2016

Learning to Select Pre-Trained Deep Representations with Bayesian Evidence Framework

We propose a Bayesian evidence framework to facilitate transfer learning from pre-trained deep convolutional neural networks (CNNs). Our framework is formulated on top of a least squares SVM (LS-SVM) classifier, which is simple and fast in both training and testing, and achieves competitive performance in practice. The regularization parameters in LS-SVM is estimated automatically without grid search and cross-validation by maximizing evidence, which is a useful measure to select the best performing CNN out of multiple candidates for transfer learning; the evidence is optimized efficiently by employing Aitken's delta-squared process, which accelerates convergence of fixed point update. The proposed Bayesian evidence framework also provides a good solution to identify the best ensemble of heterogeneous CNNs through a greedy algorithm. Our Bayesian evidence framework for transfer learning is tested on 12 visual recognition datasets and illustrates the state-of-the-art performance consistently in terms of prediction accuracy and modeling efficiency.

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arXiv2016

Gaussian Copula Variational Autoencoders for Mixed Data

The variational autoencoder (VAE) is a generative model with continuous latent variables where a pair of probabilistic encoder (bottom-up) and decoder (top-down) is jointly learned by stochastic gradient variational Bayes. We first elaborate Gaussian VAE, approximating the local covariance matrix of the decoder as an outer product of the principal direction at a position determined by a sample drawn from Gaussian distribution. We show that this model, referred to as VAE-ROC, better captures the data manifold, compared to the standard Gaussian VAE where independent multivariate Gaussian was used to model the decoder. Then we extend the VAE-ROC to handle mixed categorical and continuous data. To this end, we employ Gaussian copula to model the local dependency in mixed categorical and continuous data, leading to {\em Gaussian copula variational autoencoder} (GCVAE). As in VAE-ROC, we use the rank-one approximation for the covariance in the Gaussian copula, to capture the local dependency structure in the mixed data. Experiments on various datasets demonstrate the useful behaviour of VAE-ROC and GCVAE, compared to the standard VAE.

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arXiv2015

Tree-Guided MCMC Inference for Normalized Random Measure Mixture Models

Normalized random measures (NRMs) provide a broad class of discrete random measures that are often used as priors for Bayesian nonparametric models. Dirichlet process is a well-known example of NRMs. Most of posterior inference methods for NRM mixture models rely on MCMC methods since they are easy to implement and their convergence is well studied. However, MCMC often suffers from slow convergence when the acceptance rate is low. Tree-based inference is an alternative deterministic posterior inference method, where Bayesian hierarchical clustering (BHC) or incremental Bayesian hierarchical clustering (IBHC) have been developed for DP or NRM mixture (NRMM) models, respectively. Although IBHC is a promising method for posterior inference for NRMM models due to its efficiency and applicability to online inference, its convergence is not guaranteed since it uses heuristics that simply selects the best solution after multiple trials are made. In this paper, we present a hybrid inference algorithm for NRMM models, which combines the merits of both MCMC and IBHC. Trees built by IBHC outlines partitions of data, which guides Metropolis-Hastings procedure to employ appropriate proposals. Inheriting the nature of MCMC, our tree-guided MCMC (tgMCMC) is guaranteed to converge, and enjoys the fast convergence thanks to the effective proposals guided by trees. Experiments on both synthetic and real-world datasets demonstrate the benefit of our method.

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arXiv2015

Bayesian Hierarchical Clustering with Exponential Family: Small-Variance Asymptotics and Reducibility

Bayesian hierarchical clustering (BHC) is an agglomerative clustering method, where a probabilistic model is defined and its marginal likelihoods are evaluated to decide which clusters to merge. While BHC provides a few advantages over traditional distance-based agglomerative clustering algorithms, successive evaluation of marginal likelihoods and careful hyperparameter tuning are cumbersome and limit the scalability. In this paper we relax BHC into a non-probabilistic formulation, exploring small-variance asymptotics in conjugate-exponential models. We develop a novel clustering algorithm, referred to as relaxed BHC (RBHC), from the asymptotic limit of the BHC model that exhibits the scalability of distance-based agglomerative clustering algorithms as well as the flexibility of Bayesian nonparametric models. We also investigate the reducibility of the dissimilarity measure emerged from the asymptotic limit of the BHC model, allowing us to use scalable algorithms such as the nearest neighbor chain algorithm. Numerical experiments on both synthetic and real-world datasets demonstrate the validity and high performance of our method.

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arXiv2015

Bilinear Random Projections for Locality-Sensitive Binary Codes

Locality-sensitive hashing (LSH) is a popular data-independent indexing method for approximate similarity search, where random projections followed by quantization hash the points from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. Most of high-dimensional visual descriptors for images exhibit a natural matrix structure. When visual descriptors are represented by high-dimensional feature vectors and long binary codes are assigned, a random projection matrix requires expensive complexities in both space and time. In this paper we analyze a bilinear random projection method where feature matrices are transformed to binary codes by two smaller random projection matrices. We base our theoretical analysis on extending Raginsky and Lazebnik's result where random Fourier features are composed with random binary quantizers to form locality sensitive binary codes. To this end, we answer the following two questions: (1) whether a bilinear random projection also yields similarity-preserving binary codes; (2) whether a bilinear random projection yields performance gain or loss, compared to a large linear projection. Regarding the first question, we present upper and lower bounds on the expected Hamming distance between binary codes produced by bilinear random projections. In regards to the second question, we analyze the upper and lower bounds on covariance between two bits of binary codes, showing that the correlation between two bits is small. Numerical experiments on MNIST and Flickr45K datasets confirm the validity of our method.

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arXiv2014

Convex Optimization for Binary Classifier Aggregation in Multiclass Problems

Multiclass problems are often decomposed into multiple binary problems that are solved by individual binary classifiers whose results are integrated into a final answer. Various methods, including all-pairs (APs), one-versus-all (OVA), and error correcting output code (ECOC), have been studied, to decompose multiclass problems into binary problems. However, little study has been made to optimally aggregate binary problems to determine a final answer to the multiclass problem. In this paper we present a convex optimization method for an optimal aggregation of binary classifiers to estimate class membership probabilities in multiclass problems. We model the class membership probability as a softmax function which takes a conic combination of discrepancies induced by individual binary classifiers, as an input. With this model, we formulate the regularized maximum likelihood estimation as a convex optimization problem, which is solved by the primal-dual interior point method. Connections of our method to large margin classifiers are presented, showing that the large margin formulation can be considered as a limiting case of our convex formulation. Numerical experiments on synthetic and real-world data sets demonstrate that our method outperforms existing aggregation methods as well as direct methods, in terms of the classification accuracy and the quality of class membership probability estimates.

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arXiv2013

Learning Features with Structure-Adapting Multi-view Exponential Family Harmoniums

We proposea graphical model for multi-view feature extraction that automatically adapts its structure to achieve better representation of data distribution. The proposed model, structure-adapting multi-view harmonium (SA-MVH) has switch parameters that control the connection between hidden nodes and input views, and learn the switch parameter while training. Numerical experiments on synthetic and a real-world dataset demonstrate the useful behavior of the SA-MVH, compared to existing multi-view feature extraction methods.

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arXiv2013

Regularized Discriminant Embedding for Visual Descriptor Learning

Images can vary according to changes in viewpoint, resolution, noise, and illumination. In this paper, we aim to learn representations for an image, which are robust to wide changes in such environmental conditions, using training pairs of matching and non-matching local image patches that are collected under various environmental conditions. We present a regularized discriminant analysis that emphasizes two challenging categories among the given training pairs: (1) matching, but far apart pairs and (2) non-matching, but close pairs in the original feature space (e.g., SIFT feature space). Compared to existing work on metric learning and discriminant analysis, our method can better distinguish relevant images from irrelevant, but look-alike images.

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