arXiv subjects

Shota Saito

Publications and source records attributed to Shota Saito.

At least 37 records · Page 2Linked to original sources

arXiv2023

Multi-class Graph Clustering via Approximated Effective $p$-Resistance

This paper develops an approximation to the (effective) $p$-resistance and applies it to multi-class clustering. Spectral methods based on the graph Laplacian and its generalization to the graph $p$-Laplacian have been a backbone of non-euclidean clustering techniques. The advantage of the $p$-Laplacian is that the parameter $p$ induces a controllable bias on cluster structure. The drawback of $p$-Laplacian eigenvector based methods is that the third and higher eigenvectors are difficult to compute. Thus, instead, we are motivated to use the $p$-resistance induced by the $p$-Laplacian for clustering. For $p$-resistance, small $p$ biases towards clusters with high internal connectivity while large $p$ biases towards clusters of small "extent," that is a preference for smaller shortest-path distances between vertices in the cluster. However, the $p$-resistance is expensive to compute. We overcome this by developing an approximation to the $p$-resistance. We prove upper and lower bounds on this approximation and observe that it is exact when the graph is a tree. We also provide theoretical justification for the use of $p$-resistance for clustering. Finally, we provide experiments comparing our approximated $p$-resistance clustering to other $p$-Laplacian based methods.

cs.LG↗

arXiv2023

Prediction Algorithms Achieving Bayesian Decision Theoretical Optimality Based on Decision Trees as Data Observation Processes

In the field of decision trees, most previous studies have difficulty ensuring the statistical optimality of a prediction of new data and suffer from overfitting because trees are usually used only to represent prediction functions to be constructed from given data. In contrast, some studies, including this paper, used the trees to represent stochastic data observation processes behind given data. Moreover, they derived the statistically optimal prediction, which is robust against overfitting, based on the Bayesian decision theory by assuming a prior distribution for the trees. However, these studies still have a problem in computing this Bayes optimal prediction because it involves an infeasible summation for all division patterns of a feature space, which is represented by the trees and some parameters. In particular, an open problem is a summation with respect to combinations of division axes, i.e., the assignment of features to inner nodes of the tree. We solve this by a Markov chain Monte Carlo method, whose step size is adaptively tuned according to a posterior distribution for the trees.

cs.LG↗

arXiv2023

(1+1)-CMA-ES with Margin for Discrete and Mixed-Integer Problems

The covariance matrix adaptation evolution strategy (CMA-ES) is an efficient continuous black-box optimization method. The CMA-ES possesses many attractive features, including invariance properties and a well-tuned default hyperparameter setting. Moreover, several components to specialize the CMA-ES have been proposed, such as noise handling and constraint handling. To utilize these advantages in mixed-integer optimization problems, the CMA-ES with margin has been proposed. The CMA-ES with margin prevents the premature convergence of discrete variables by the margin correction, in which the distribution parameters are modified to leave the generation probability for changing the discrete variable. The margin correction has been applied to ($μ/μ_\mathrm{w}$,$λ$)-CMA-ES, while this paper introduces the margin correction into (1+1)-CMA-ES, an elitist version of CMA-ES. The (1+1)-CMA-ES is often advantageous for unimodal functions and can be computationally less expensive. To tackle the performance deterioration on mixed-integer optimization, we use the discretized elitist solution as the mean of the sampling distribution and modify the margin correction not to move the elitist solution. The numerical simulation using benchmark functions on mixed-integer, integer, and binary domains shows that (1+1)-CMA-ES with margin outperforms the CMA-ES with margin and is better than or comparable with several specialized methods to a particular search domain.

cs.NE↗

arXiv2023

CMA-ES with Margin: Lower-Bounding Marginal Probability for Mixed-Integer Black-Box Optimization

This study targets the mixed-integer black-box optimization (MI-BBO) problem where continuous and integer variables should be optimized simultaneously. The CMA-ES, our focus in this study, is a population-based stochastic search method that samples solution candidates from a multivariate Gaussian distribution (MGD), which shows excellent performance in continuous BBO. The parameters of MGD, mean and (co)variance, are updated based on the evaluation value of candidate solutions in the CMA-ES. If the CMA-ES is applied to the MI-BBO with straightforward discretization, however, the variance corresponding to the integer variables becomes much smaller than the granularity of the discretization before reaching the optimal solution, which leads to the stagnation of the optimization. In particular, when binary variables are included in the problem, this stagnation more likely occurs because the granularity of the discretization becomes wider, and the existing modification to the CMA-ES does not address this stagnation. To overcome these limitations, we propose a simple modification of the CMA-ES based on lower-bounding the marginal probabilities associated with the generation of integer variables in the MGD. The numerical experiments on the MI-BBO benchmark problems demonstrate the efficiency and robustness of the proposed method.

cs.NE↗

arXiv2022

Direct Observation and Quantitative Measurement of OH Radical Desorption During the Ultraviolet Photolysis of Liquid Nonanoic Acid

Ultraviolet (UV) photolysis of fatty acid surfactants which cover the surfaces of atmospheric liquid aerosols and are found in the oceans such as nonanoic acid (NA) has recently been suggested as a source of hydroxyl (OH) radicals in the troposphere. We used laser-induced fluorescence to directly observe OH radicals desorbed from the surface of neat liquid NA as a primary photoproduct following 213 nm irradiation. The upper limit of photoreaction cross section for the OH radical desorption was estimated to be 9.0(4.1) $\times$ 10$^{-22}$ cm$^2$, which is only 1.2$\pm$0.8% of the photoreaction cross section established for the photolysis of gas-phase acetic acid monomers. Vibrational sum-frequency generation spectroscopy for liquid NA revealed the hydrogen-bonded, cyclic, dimer structure of the NA molecules at the liquid surface. This dimerization can inhibit the formation of OH radicals and lead the present low photochemical reactivity of liquid NA.

physics.ao-ph↗

arXiv2022

Neural Architecture Search for Improving Latency-Accuracy Trade-off in Split Computing

This paper proposes a neural architecture search (NAS) method for split computing. Split computing is an emerging machine-learning inference technique that addresses the privacy and latency challenges of deploying deep learning in IoT systems. In split computing, neural network models are separated and cooperatively processed using edge servers and IoT devices via networks. Thus, the architecture of the neural network model significantly impacts the communication payload size, model accuracy, and computational load. In this paper, we address the challenge of optimizing neural network architecture for split computing. To this end, we proposed NASC, which jointly explores optimal model architecture and a split point to achieve higher accuracy while meeting latency requirements (i.e., smaller total latency of computation and communication than a certain threshold). NASC employs a one-shot NAS that does not require repeating model training for a computationally efficient architecture search. Our performance evaluation using hardware (HW)-NAS-Bench of benchmark data demonstrates that the proposed NASC can improve the ``communication latency and model accuracy" trade-off, i.e., reduce the latency by approximately 40-60% from the baseline, with slight accuracy degradation.

cs.LG↗

arXiv2022

Hypergraph Modeling via Spectral Embedding Connection: Hypergraph Cut, Weighted Kernel $k$-means, and Heat Kernel

We propose a theoretical framework of multi-way similarity to model real-valued data into hypergraphs for clustering via spectral embedding. For graph cut based spectral clustering, it is common to model real-valued data into graph by modeling pairwise similarities using kernel function. This is because the kernel function has a theoretical connection to the graph cut. For problems where using multi-way similarities are more suitable than pairwise ones, it is natural to model as a hypergraph, which is generalization of a graph. However, although the hypergraph cut is well-studied, there is not yet established a hypergraph cut based framework to model multi-way similarity. In this paper, we formulate multi-way similarities by exploiting the theoretical foundation of kernel function. We show a theoretical connection between our formulation and hypergraph cut in two ways, generalizing both weighted kernel $k$-means and the heat kernel, by which we justify our formulation. We also provide a fast algorithm for spectral clustering. Our algorithm empirically shows better performance than existing graph and other heuristic modeling methods.

cs.LG↗

arXiv2022

Efficient Search of Multiple Neural Architectures with Different Complexities via Importance Sampling

Neural architecture search (NAS) aims to automate architecture design processes and improve the performance of deep neural networks. Platform-aware NAS methods consider both performance and complexity and can find well-performing architectures with low computational resources. Although ordinary NAS methods result in tremendous computational costs owing to the repetition of model training, one-shot NAS, which trains the weights of a supernetwork containing all candidate architectures only once during the search process, has been reported to result in a lower search cost. This study focuses on the architecture complexity-aware one-shot NAS that optimizes the objective function composed of the weighted sum of two metrics, such as the predictive performance and number of parameters. In existing methods, the architecture search process must be run multiple times with different coefficients of the weighted sum to obtain multiple architectures with different complexities. This study aims at reducing the search cost associated with finding multiple architectures. The proposed method uses multiple distributions to generate architectures with different complexities and updates each distribution using the samples obtained from multiple distributions based on importance sampling. The proposed method allows us to obtain multiple architectures with different complexities in a single architecture search, resulting in reducing the search cost. The proposed method is applied to the architecture search of convolutional neural networks on the CIAFR-10 and ImageNet datasets. Consequently, compared with baseline methods, the proposed method finds multiple architectures with varying complexities while requiring less computational effort.

cs.NE↗

arXiv2022

Probability Distribution on Rooted Trees

The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical expressive capability causes a problem in tree selection to avoid overfitting. One unified approach to solve this is a Bayesian approach, on which the rooted tree is regarded as a random variable and a direct loss function can be assumed on the selected model or the predicted value for a new data point. However, all the previous studies on this approach are based on the probability distribution on full trees, to the best of our knowledge. In this paper, we propose a generalized probability distribution for any rooted trees in which only the maximum number of child nodes and the maximum depth are fixed. Furthermore, we derive recursive methods to evaluate the characteristics of the probability distribution without any approximations.

cs.LG↗

arXiv2022

Probability Distribution on Full Rooted Trees

The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is not a random variable; as such, model selection to avoid overfitting becomes problematic. A method to solve this problem is to assume a prior distribution on the full rooted trees. This enables the optimal model selection based on the Bayes decision theory. For example, by assigning a low prior probability to a complex model, the maximum a posteriori estimator prevents the selection of the complex one. Furthermore, we can average all the models weighted by their posteriors. In this paper, we propose a probability distribution on a set of full rooted trees. Its parametric representation is suitable for calculating the properties of our distribution using recursive functions, such as the mode, expectation, and posterior distribution. Although such distributions have been proposed in previous studies, they are only applicable to specific applications. Therefore, we extract their mathematically essential components and derive new generalized methods to calculate the expectation, posterior distribution, etc.

stat.ML↗

arXiv2021

An Efficient Bayes Coding Algorithm for the Non-Stationary Source in Which Context Tree Model Varies from Interval to Interval

The context tree source is a source model in which the occurrence probability of symbols is determined from a finite past sequence, and is a broader class of sources that includes i.i.d. and Markov sources. The proposed source model in this paper represents that a subsequence in each interval is generated from a different context tree model. The Bayes code for such sources requires weighting of the posterior probability distributions for the change patterns of the context tree source and for all possible context tree models. Therefore, the challenge is how to reduce this exponential order computational complexity. In this paper, we assume a special class of prior probability distribution of change patterns and context tree models, and propose an efficient Bayes coding algorithm whose computational complexity is the polynomial order.

cs.IT↗

arXiv2021

Evaluation of Error Probability of Classification Based on the Analysis of the Bayes Code: Extension and Example

Suppose that we have two training sequences generated by parametrized distributions $P_{θ^*}$ and $P_{ξ^*}$, where $θ^*$ and $ξ^*$ are unknown true parameters. Given training sequences, we study the problem of classifying whether a test sequence was generated according to $P_{θ^*}$ or $P_{ξ^*}$. This problem can be thought of as a hypothesis testing problem and our aim is to analyze the weighted sum of type-I and type-II error probabilities. Utilizing the analysis of the codeword lengths of the Bayes code, our previous study derived more refined bounds on the error probability than known previously. However, our previous study had the following deficiencies: i) the prior distributions of $θ$ and $ξ$ are the same; ii) the prior distributions of two hypotheses are uniform; iii) no numerical calculation at finite blocklength. This study solves these problems. We remove the restrictions i) and ii) and derive more general results than obtained previously. To deal with problem iii), we perform a numerical calculation for a concrete model.

cs.IT↗

arXiv2019

Controlling Model Complexity in Probabilistic Model-Based Dynamic Optimization of Neural Network Structures

A method of simultaneously optimizing both the structure of neural networks and the connection weights in a single training loop can reduce the enormous computational cost of neural architecture search. We focus on the probabilistic model-based dynamic neural network structure optimization that considers the probability distribution of structure parameters and simultaneously optimizes both the distribution parameters and connection weights based on gradient methods. Since the existing algorithm searches for the structures that only minimize the training loss, this method might find overly complicated structures. In this paper, we propose the introduction of a penalty term to control the model complexity of obtained structures. We formulate a penalty term using the number of weights or units and derive its analytical natural gradient. The proposed method minimizes the objective function injected the penalty term based on the stochastic gradient descent. We apply the proposed method in the unit selection of a fully-connected neural network and the connection selection of a convolutional neural network. The experimental results show that the proposed method can control model complexity while maintaining performance.

cs.NE↗

arXiv2019

Adaptive Stochastic Natural Gradient Method for One-Shot Neural Architecture Search

High sensitivity of neural architecture search (NAS) methods against their input such as step-size (i.e., learning rate) and search space prevents practitioners from applying them out-of-the-box to their own problems, albeit its purpose is to automate a part of tuning process. Aiming at a fast, robust, and widely-applicable NAS, we develop a generic optimization framework for NAS. We turn a coupled optimization of connection weights and neural architecture into a differentiable optimization by means of stochastic relaxation. It accepts arbitrary search space (widely-applicable) and enables to employ a gradient-based simultaneous optimization of weights and architecture (fast). We propose a stochastic natural gradient method with an adaptive step-size mechanism built upon our theoretical investigation (robust). Despite its simplicity and no problem-dependent parameter tuning, our method exhibited near state-of-the-art performances with low computational budgets both on image classification and inpainting tasks.

cs.LG↗

arXiv2019

Non-Asymptotic Fundamental Limits of Guessing Subject to Distortion

This paper investigates the problem of guessing subject to distortion, which was introduced by Arikan and Merhav. While the primary concern of the previous study was asymptotic analysis, our primary concern is non-asymptotic analysis. We prove non-asymptotic achievability and converse bounds of the moment of the number of guesses without side information (resp. with side information) by using a quantity based on the Rényi entropy (resp. the Arimoto-Rényi conditional entropy). Also, we introduce an error probability and show similar results. Further, from our bounds, we derive a single-letter characterization of the asymptotic exponent of guessing moment for a stationary memoryless source.

cs.IT↗

arXiv2018

Variable-Length Lossy Compression Allowing Positive Overflow and Excess Distortion Probabilities

This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal rate are established by a new quantity based on the smooth max entropy (the smooth Rényi entropy of order zero). To derive the achievability bounds, we give an explicit code construction based on a distortion ball instead of using the random coding argument. The basic idea of the code construction is similar to the optimal code construction in the variable-length lossless source coding. Our achievability bounds are slightly different, depending on whether the encoder is stochastic or deterministic. One-shot results yield a general formula of the optimal rate for blocklength $n$. In addition, our general formula is applied to asymptotic analysis for a stationary memoryless source. As a result, we derive a single-letter characterization of the optimal rate by using the rate-distortion and rate-dispersion functions.

cs.IT↗

arXiv2018

Parameterless Stochastic Natural Gradient Method for Discrete Optimization and its Application to Hyper-Parameter Optimization for Neural Network

Black box discrete optimization (BBDO) appears in wide range of engineering tasks. Evolutionary or other BBDO approaches have been applied, aiming at automating necessary tuning of system parameters, such as hyper parameter tuning of machine learning based systems when being installed for a specific task. However, automation is often jeopardized by the need of strategy parameter tuning for BBDO algorithms. An expert with the domain knowledge must undergo time-consuming strategy parameter tuning. This paper proposes a parameterless BBDO algorithm based on information geometric optimization, a recent framework for black box optimization using stochastic natural gradient. Inspired by some theoretical implications, we develop an adaptation mechanism for strategy parameters of the stochastic natural gradient method for discrete search domains. The proposed algorithm is evaluated on commonly used test problems. It is further extended to two examples of simultaneous optimization of the hyper parameters and the connection weights of deep learning models, leading to a faster optimization than the existing approaches without any effort of parameter tuning.

cs.LG↗

arXiv2018

Variable-Length Intrinsic Randomness Allowing Positive Value of the Average Variational Distance

This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length resolvability. Previous study has derived the general formula of the $ε$-variable-length resolvability. We derive the general formula of the $ε$-variable-length intrinsic randomness. Namely, we characterize the supremum of the mean length under the constraint that the value of the average variational distance is smaller than or equal to a constant $ε$. Our result clarifies a dual relationship between the general formula of $ε$-variable-length resolvability and that of $ε$-variable-length intrinsic randomness. We also derive a lower bound of the quantity characterizing our general formula.

cs.IT↗