arXiv subjects

Makoto Yamada

Publications and source records attributed to Makoto Yamada.

At least 55 records · Page 3Linked to original sources

arXiv2022

Scale dependant layer for self-supervised nuclei encoding

Recent developments in self-supervised learning give us the possibility to further reduce human intervention in multi-step pipelines where the focus evolves around particular objects of interest. In the present paper, the focus lays in the nuclei in histopathology images. In particular we aim at extracting cellular information in an unsupervised manner for a downstream task. As nuclei present themselves in a variety of sizes, we propose a new Scale-dependant convolutional layer to bypass scaling issues when resizing nuclei. On three nuclei datasets, we benchmark the following methods: handcrafted, pre-trained ResNet, supervised ResNet and self-supervised features. We show that the proposed convolution layer boosts performance and that this layer combined with Barlows-Twins allows for better nuclei encoding compared to the supervised paradigm in the low sample setting and outperforms all other proposed unsupervised methods. In addition, we extend the existing TNBC dataset to incorporate nuclei class annotation in order to enrich and publicly release a small sample setting dataset for nuclei segmentation and classification.

cs.CV↗

arXiv2022

Approximating 1-Wasserstein Distance with Trees

Wasserstein distance, which measures the discrepancy between distributions, shows efficacy in various types of natural language processing (NLP) and computer vision (CV) applications. One of the challenges in estimating Wasserstein distance is that it is computationally expensive and does not scale well for many distribution comparison tasks. In this paper, we aim to approximate the 1-Wasserstein distance by the tree-Wasserstein distance (TWD), where TWD is a 1-Wasserstein distance with tree-based embedding and can be computed in linear time with respect to the number of nodes on a tree. More specifically, we propose a simple yet efficient L1-regularized approach to learning the weights of the edges in a tree. To this end, we first show that the 1-Wasserstein approximation problem can be formulated as a distance approximation problem using the shortest path distance on a tree. We then show that the shortest path distance can be represented by a linear model and can be formulated as a Lasso-based regression problem. Owing to the convex formulation, we can obtain a globally optimal solution efficiently. Moreover, we propose a tree-sliced variant of these methods. Through experiments, we demonstrated that the weighted TWD can accurately approximate the original 1-Wasserstein distance.

stat.ML↗

arXiv2022

Re-evaluating Word Mover's Distance

The word mover's distance (WMD) is a fundamental technique for measuring the similarity of two documents. As the crux of WMD, it can take advantage of the underlying geometry of the word space by employing an optimal transport formulation. The original study on WMD reported that WMD outperforms classical baselines such as bag-of-words (BOW) and TF-IDF by significant margins in various datasets. In this paper, we point out that the evaluation in the original study could be misleading. We re-evaluate the performances of WMD and the classical baselines and find that the classical baselines are competitive with WMD if we employ an appropriate preprocessing, i.e., L1 normalization. In addition, we introduce an analogy between WMD and L1-normalized BOW and find that not only the performance of WMD but also the distance values resemble those of BOW in high dimensional spaces.

cs.LG↗

arXiv2022

Feature Selection for Discovering Distributional Treatment Effect Modifiers

Finding the features relevant to the difference in treatment effects is essential to unveil the underlying causal mechanisms. Existing methods seek such features by measuring how greatly the feature attributes affect the degree of the {\it conditional average treatment effect} (CATE). However, these methods may overlook important features because CATE, a measure of the average treatment effect, cannot detect differences in distribution parameters other than the mean (e.g., variance). To resolve this weakness of existing methods, we propose a feature selection framework for discovering {\it distributional treatment effect modifiers}. We first formulate a feature importance measure that quantifies how strongly the feature attributes influence the discrepancy between potential outcome distributions. Then we derive its computationally efficient estimator and develop a feature selection algorithm that can control the type I error rate to the desired level. Experimental results show that our framework successfully discovers important features and outperforms the existing mean-based method.

cs.LG↗

arXiv2022

Communication Compression for Decentralized Learning with Operator Splitting Methods

In decentralized learning, operator splitting methods using a primal-dual formulation (e.g., the Edge-Consensus Learning (ECL)) has been shown to be robust to heterogeneous data and has attracted significant attention in recent years. However, in the ECL, a node needs to exchange dual variables with its neighbors. These exchanges incur significant communication costs. For the Gossip-based algorithms, many compression methods have been proposed, but these Gossip-based algorithm do not perform well when the data distribution held by each node is statistically heterogeneous. In this work, we propose the novel framework of the compression methods for the ECL, called the Communication Compressed ECL (C-ECL). Specifically, we reformulate the update formulas of the ECL, and propose to compress the update values of the dual variables. We demonstrate experimentally that the C-ECL can achieve a nearly equivalent performance with fewer parameter exchanges than the ECL. Moreover, we demonstrate that the C-ECL is more robust to heterogeneous data than the Gossip-based algorithms.

cs.LG↗

arXiv2022

Constant Time Graph Neural Networks

The recent advancements in graph neural networks (GNNs) have led to state-of-the-art performances in various applications, including chemo-informatics, question-answering systems, and recommender systems. However, scaling up these methods to huge graphs, such as social networks and Web graphs, remains a challenge. In particular, the existing methods for accelerating GNNs either are not theoretically guaranteed in terms of the approximation error or incur at least a linear time computation cost. In this study, we reveal the query complexity of the uniform node sampling scheme for Message Passing Neural Networks, including GraphSAGE, graph attention networks (GATs), and graph convolutional networks (GCNs). Surprisingly, our analysis reveals that the complexity of the node sampling method is completely independent of the number of the nodes, edges, and neighbors of the input and depends only on the error tolerance and confidence probability while providing a theoretical guarantee for the approximation error. To the best of our knowledge, this is the first paper to provide a theoretical guarantee of approximation for GNNs within constant time. Through experiments with synthetic and real-world datasets, we investigated the speed and precision of the node sampling scheme and validated our theoretical results.

cs.LG↗

arXiv2022

Fixed Support Tree-Sliced Wasserstein Barycenter

The Wasserstein barycenter has been widely studied in various fields, including natural language processing, and computer vision. However, it requires a high computational cost to solve the Wasserstein barycenter problem because the computation of the Wasserstein distance requires a quadratic time with respect to the number of supports. By contrast, the Wasserstein distance on a tree, called the tree-Wasserstein distance, can be computed in linear time and allows for the fast comparison of a large number of distributions. In this study, we propose a barycenter under the tree-Wasserstein distance, called the fixed support tree-Wasserstein barycenter (FS-TWB) and its extension, called the fixed support tree-sliced Wasserstein barycenter (FS-TSWB). More specifically, we first show that the FS-TWB and FS-TSWB problems are convex optimization problems and can be solved by using the projected subgradient descent. Moreover, we propose a more efficient algorithm to compute the subgradient and objective function value by using the properties of tree-Wasserstein barycenter problems. Through real-world experiments, we show that, by using the proposed algorithm, the FS-TWB and FS-TSWB can be solved two orders of magnitude faster than the original Wasserstein barycenter.

cs.AI↗

arXiv2022

Nys-Newton: Nyström-Approximated Curvature for Stochastic Optimization

Second-order optimization methods are among the most widely used optimization approaches for convex optimization problems, and have recently been used to optimize non-convex optimization problems such as deep learning models. The widely used second-order optimization methods such as quasi-Newton methods generally provide curvature information by approximating the Hessian using the secant equation. However, the secant equation becomes insipid in approximating the Newton step owing to its use of the first-order derivatives. In this study, we propose an approximate Newton sketch-based stochastic optimization algorithm for large-scale empirical risk minimization. Specifically, we compute a partial column Hessian of size ($d\times m$) with $m\ll d$ randomly selected variables, then use the \emph{Nyström method} to better approximate the full Hessian matrix. To further reduce the computational complexity per iteration, we directly compute the update step ($Δ\boldsymbol{w}$) without computing and storing the full Hessian or its inverse. We then integrate our approximated Hessian with stochastic gradient descent and stochastic variance-reduced gradient methods. The results of numerical experiments on both convex and non-convex functions show that the proposed approach was able to obtain a better approximation of Newton\textquotesingle s method, exhibiting performance competitive with that of state-of-the-art first-order and stochastic quasi-Newton methods. Furthermore, we provide a theoretical convergence analysis for convex functions.

math.OC↗

arXiv2021

Adversarial Regression with Doubly Non-negative Weighting Matrices

Many machine learning tasks that involve predicting an output response can be solved by training a weighted regression model. Unfortunately, the predictive power of this type of models may severely deteriorate under low sample sizes or under covariate perturbations. Reweighting the training samples has aroused as an effective mitigation strategy to these problems. In this paper, we propose a novel and coherent scheme for kernel-reweighted regression by reparametrizing the sample weights using a doubly non-negative matrix. When the weighting matrix is confined in an uncertainty set using either the log-determinant divergence or the Bures-Wasserstein distance, we show that the adversarially reweighted estimate can be solved efficiently using first-order methods. Numerical experiments show that our reweighting strategy delivers promising results on numerous datasets.

stat.ML↗

arXiv2021

Supervised Tree-Wasserstein Distance

To measure the similarity of documents, the Wasserstein distance is a powerful tool, but it requires a high computational cost. Recently, for fast computation of the Wasserstein distance, methods for approximating the Wasserstein distance using a tree metric have been proposed. These tree-based methods allow fast comparisons of a large number of documents; however, they are unsupervised and do not learn task-specific distances. In this work, we propose the Supervised Tree-Wasserstein (STW) distance, a fast, supervised metric learning method based on the tree metric. Specifically, we rewrite the Wasserstein distance on the tree metric by the parent-child relationships of a tree and formulate it as a continuous optimization problem using a contrastive loss. Experimentally, we show that the STW distance can be computed fast, and improves the accuracy of document classification tasks. Furthermore, the STW distance is formulated by matrix multiplications, runs on a GPU, and is suitable for batch processing. Therefore, we show that the STW distance is extremely efficient when comparing a large number of documents.

cs.LG↗

arXiv2021

LSMI-Sinkhorn: Semi-supervised Mutual Information Estimation with Optimal Transport

Estimating mutual information is an important statistics and machine learning problem. To estimate the mutual information from data, a common practice is preparing a set of paired samples $\{(\mathbf{x}_i,\mathbf{y}_i)\}_{i=1}^n \stackrel{\mathrm{i.i.d.}}{\sim} p(\mathbf{x},\mathbf{y})$. However, in many situations, it is difficult to obtain a large number of data pairs. To address this problem, we propose the semi-supervised Squared-loss Mutual Information (SMI) estimation method using a small number of paired samples and the available unpaired ones. We first represent SMI through the density ratio function, where the expectation is approximated by the samples from marginals and its assignment parameters. The objective is formulated using the optimal transport problem and quadratic programming. Then, we introduce the Least-Squares Mutual Information with Sinkhorn (LSMI-Sinkhorn) algorithm for efficient optimization. Through experiments, we first demonstrate that the proposed method can estimate the SMI without a large number of paired samples. Then, we show the effectiveness of the proposed LSMI-Sinkhorn algorithm on various types of machine learning problems such as image matching and photo album summarization. Code can be found at https://github.com/csyanbin/LSMI-Sinkhorn.

stat.ML↗

arXiv2021

Post-selection inference with HSIC-Lasso

Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection inference. Indeed, the selected features can be significantly flawed when the selection procedure is not accounted for. We propose a selective inference procedure using the so-called model-free "HSIC-Lasso" based on the framework of truncated Gaussians combined with the polyhedral lemma. We then develop an algorithm, which allows for low computational costs and provides a selection of the regularisation parameter. The performance of our method is illustrated by both artificial and real-world data based experiments, which emphasise a tight control of the type-I error, even for small sample sizes.

math.ST↗

arXiv2021

Optimal Transport Kernels for Sequential and Parallel Neural Architecture Search

Neural architecture search (NAS) automates the design of deep neural networks. One of the main challenges in searching complex and non-continuous architectures is to compare the similarity of networks that the conventional Euclidean metric may fail to capture. Optimal transport (OT) is resilient to such complex structure by considering the minimal cost for transporting a network into another. However, the OT is generally not negative definite which may limit its ability to build the positive-definite kernels required in many kernel-dependent frameworks. Building upon tree-Wasserstein (TW), which is a negative definite variant of OT, we develop a novel discrepancy for neural architectures, and demonstrate it within a Gaussian process surrogate model for the sequential NAS settings. Furthermore, we derive a novel parallel NAS, using quality k-determinantal point process on the GP posterior, to select diverse and high-performing architectures from a discrete set of candidates. Empirically, we demonstrate that our TW-based approaches outperform other baselines in both sequential and parallel NAS.

cs.LG↗

arXiv2021

Computationally Efficient Wasserstein Loss for Structured Labels

The problem of estimating the probability distribution of labels has been widely studied as a label distribution learning (LDL) problem, whose applications include age estimation, emotion analysis, and semantic segmentation. We propose a tree-Wasserstein distance regularized LDL algorithm, focusing on hierarchical text classification tasks. We propose predicting the entire label hierarchy using neural networks, where the similarity between predicted and true labels is measured using the tree-Wasserstein distance. Through experiments using synthetic and real-world datasets, we demonstrate that the proposed method successfully considers the structure of labels during training, and it compares favorably with the Sinkhorn algorithm in terms of computation time and memory usage.

cs.LG↗

arXiv2021

Fast and Robust Comparison of Probability Measures in Heterogeneous Spaces

Comparing two probability measures supported on heterogeneous spaces is an increasingly important problem in machine learning. Such problems arise when comparing for instance two populations of biological cells, each described with its own set of features, or when looking at families of word embeddings trained across different corpora/languages. For such settings, the Gromov Wasserstein (GW) distance is often presented as the gold standard. GW is intuitive, as it quantifies whether one measure can be isomorphically mapped to the other. However, its exact computation is intractable, and most algorithms that claim to approximate it remain expensive. Building on \cite{memoli-2011}, who proposed to represent each point in each distribution as the 1D distribution of its distances to all other points, we introduce in this paper the Anchor Energy (AE) and Anchor Wasserstein (AW) distances, which are respectively the energy and Wasserstein distances instantiated on such representations. Our main contribution is to propose a sweep line algorithm to compute AE \emph{exactly} in log-quadratic time, where a naive implementation would be cubic. This is quasi-linear w.r.t. the description of the problem itself. Our second contribution is the proposal of robust variants of AE and AW that uses rank statistics rather than the original distances. We show that AE and AW perform well in various experimental settings at a fraction of the computational cost of popular GW approximations. Code is available at \url{https://github.com/joisino/anchor-energy}.

stat.ML↗

arXiv2021

Dynamic Sasvi: Strong Safe Screening for Norm-Regularized Least Squares

A recently introduced technique for a sparse optimization problem called "safe screening" allows us to identify irrelevant variables in the early stage of optimization. In this paper, we first propose a flexible framework for safe screening based on the Fenchel-Rockafellar duality and then derive a strong safe screening rule for norm-regularized least squares by the framework. We call the proposed screening rule for norm-regularized least squares "dynamic Sasvi" because it can be interpreted as a generalization of Sasvi. Unlike the original Sasvi, it does not require the exact solution of a more strongly regularized problem; hence, it works safely in practice. We show that our screening rule can eliminate more features and increase the speed of the solver in comparison with other screening rules both theoretically and experimentally.

stat.ML↗

arXiv2021

Random Features Strengthen Graph Neural Networks

Graph neural networks (GNNs) are powerful machine learning models for various graph learning tasks. Recently, the limitations of the expressive power of various GNN models have been revealed. For example, GNNs cannot distinguish some non-isomorphic graphs and they cannot learn efficient graph algorithms. In this paper, we demonstrate that GNNs become powerful just by adding a random feature to each node. We prove that the random features enable GNNs to learn almost optimal polynomial-time approximation algorithms for the minimum dominating set problem and maximum matching problem in terms of approximation ratios. The main advantage of our method is that it can be combined with off-the-shelf GNN models with slight modifications. Through experiments, we show that the addition of random features enables GNNs to solve various problems that normal GNNs, including the graph convolutional networks (GCNs) and graph isomorphism networks (GINs), cannot solve.

cs.LG↗

arXiv2021

Fast Unbalanced Optimal Transport on a Tree

This study examines the time complexities of the unbalanced optimal transport problems from an algorithmic perspective for the first time. We reveal which problems in unbalanced optimal transport can/cannot be solved efficiently. Specifically, we prove that the Kantorovich Rubinstein distance and optimal partial transport in the Euclidean metric cannot be computed in strongly subquadratic time under the strong exponential time hypothesis. Then, we propose an algorithm that solves a more general unbalanced optimal transport problem exactly in quasi-linear time on a tree metric. The proposed algorithm processes a tree with one million nodes in less than one second. Our analysis forms a foundation for the theoretical study of unbalanced optimal transport algorithms and opens the door to the applications of unbalanced optimal transport to million-scale datasets.

cs.LG↗