Seungjin Choi

Jungtaek Kim, Seungjin Choi

Sequential model-based optimization sequentially selects a candidate point by constructing a surrogate model with the history of evaluations, to solve a black-box optimization problem. Gaussian process (GP) regression is a popular choice as a surrogate model, because of its capability of calculating prediction uncertainty analytically. On the other hand, an ensemble of randomized trees is another option and has practical merits over GPs due to its scalability and easiness of handling continuous/discrete mixed variables. In this paper we revisit various ensembles of randomized trees to investigate their behavior in the perspective of prediction uncertainty estimation. Then, we propose a new way of constructing an ensemble of randomized trees, referred to as BwO forest, where bagging with oversampling is employed to construct bootstrapped samples that are used to build randomized trees with random splitting. Experimental results demonstrate the validity and good performance of BwO forest over existing tree-based models in various circumstances.

Jungtaek Kim, Seungjin Choi, Minsu Cho

Bayesian optimization is a popular method for solving the problem of global optimization of an expensive-to-evaluate black-box function. It relies on a probabilistic surrogate model of the objective function, upon which an acquisition function is built to determine where next to evaluate the objective function. In general, Bayesian optimization with Gaussian process regression operates on a continuous space. When input variables are categorical or discrete, an extra care is needed. A common approach is to use one-hot encoded or Boolean representation for categorical variables which might yield a combinatorial explosion problem. In this paper we present a method for Bayesian optimization in a combinatorial space, which can operate well in a large combinatorial space. The main idea is to use a random mapping which embeds the combinatorial space into a convex polytope in a continuous space, on which all essential process is performed to determine a solution to the black-box optimization in the combinatorial space. We describe our combinatorial Bayesian optimization algorithm and present its regret analysis. Numerical experiments demonstrate that our method shows satisfactory performance compared to existing methods.

Yoonho Lee, Wonjae Kim, Wonpyo Park et al.

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.

Saehoon Kim, Seungjin Choi

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.

Juho Lee, Seungjin Choi

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.

Sunho Park, TaeHyun Hwang, Seungjin Choi

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.

Yoonseop Kang, Seungjin Choi

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.