arXiv subjects

Sewon Park

Publications and source records attributed to Sewon Park.

18 recordsLinked to original sources

arXiv2026

Posterior Contraction of L\'evy Adaptive B-spline Regression in Besov Spaces

We investigate the asymptotic properties of the L\'evy Adaptive B-spline (LABS) regression model, a Bayesian nonparametric method that incorporates B-spline kernels into the L\'evy Adaptive Regression Kernel (LARK) model. LABS applies splines of varying degrees with independently defined knots, yielding a flexible model class capable of adapting to irregular and locally structured features of the true function. Within the nonparametric regression framework with univariate random design and Gaussian errors, we establish that the LABS posterior contracts around the true function in Besov classes at nearly minimax-optimal rates, up to a logarithmic factor, while adapting automatically to unknown smoothness. This study contributes to filling a gap in the literature, where theoretical results on posterior contraction of the LARK model in Besov spaces remain scarce. Simulation experiments on standard test functions in Besov spaces, including Blocks, Bumps, HeaviSine, and Doppler, complement the theoretical results and demonstrate the practical utility of LABS.

stat.ML↗

arXiv2025

TSGM: Regular and Irregular Time-series Generation using Score-based Generative Models

Score-based generative models (SGMs) have demonstrated unparalleled sampling quality and diversity in numerous fields, such as image generation, voice synthesis, and tabular data synthesis, etc. Inspired by those outstanding results, we apply SGMs to synthesize time-series by learning its conditional score function. To this end, we present a conditional score network for time-series synthesis, deriving a denoising score matching loss tailored for our purposes. In particular, our presented denoising score matching loss is the conditional denoising score matching loss for time-series synthesis. In addition, our framework is such flexible that both regular and irregular time-series can be synthesized with minimal changes to our model design. Finally, we obtain exceptional synthesis performance on various time-series datasets, achieving state-of-the-art sampling diversity and quality.

cs.LG↗

arXiv2025

Tunable Photodetectors Based on 2D Hybrid Structures from Transition Metal Dichalcogenides and Photochromic Molecules

This article reviews recent progress in two-dimensional (2D) hybrid structures that integrate transition metal dichalcogenides (TMDs) with photochromic molecules for photodetector applications. Atomically thin TMD semiconductors offer strong light-matter interaction, tunable bandgaps, and efficient carrier transport, making them suitable for photodetectors. Photochromic molecules, capable of reversible structural changes in response to external light, can modulate their chemical, optical, and electronic properties. The combinations of various light-adaptive compounds and TMDs provide a versatile platform to explore optically programmable behaviors such as wavelength-selective photoresponse, nonvolatile switching, and multilevel memory characteristics. TMD/photochromic hybrids offer new functional capabilities that are difficult to achieve with either component alone. This mini-review summarizes material properties, interfacial integration strategies, working mechanisms, and representative device demonstrations. We conclude by highlighting future research directions toward the practical implementation of photoresponsive hybrid systems in high-performance adaptive optoelectronics.

cond-mat.mes-hall↗

arXiv2025

Eigenstructure inference for high-dimensional covariance with generalized shrinkage inverse-Wishart prior

In multivariate statistics, estimating the covariance matrix is essential for understanding the interdependence among variables. In high-dimensional settings, where the number of covariates increases with the sample size, it is well known that the eigenstructure of the sample covariance matrix is inconsistent. The inverse-Wishart prior, a standard choice for covariance estimation in Bayesian inference, also suffers from posterior inconsistency. To address the issue of eigenvalue dispersion in high-dimensional settings, the shrinkage inverse-Wishart (SIW) prior has recently been proposed. Despite its conceptual appeal and empirical success, the asymptotic justification for the SIW prior has remained limited. In this paper, we propose a generalized shrinkage inverse-Wishart (gSIW) prior for high-dimensional covariance modeling. By extending the SIW framework, the gSIW prior accommodates a broader class of prior distributions and facilitates the derivation of theoretical properties under specific parameter choices. In particular, under the spiked covariance assumption, we establish the asymptotic behavior of the posterior distribution for both eigenvalues and eigenvectors by directly evaluating the posterior expectations for two sets of parameter choices. This direct evaluation provides insights into the large-sample behavior of the posterior that cannot be obtained through general posterior asymptotic theorems. Finally, simulation studies illustrate that the proposed prior provides accurate estimation of the eigenstructure, particularly for spiked eigenvalues, achieving narrower credible intervals and higher coverage probabilities compared to existing methods. For spiked eigenvectors, the performance is generally comparable to that of competing approaches, including the sample covariance.

math.ST↗

arXiv2025

Possibility for Proactive Anomaly Detection

Time-series anomaly detection, which detects errors and failures in a workflow, is one of the most important topics in real-world applications. The purpose of time-series anomaly detection is to reduce potential damages or losses. However, existing anomaly detection models detect anomalies through the error between the model output and the ground truth (observed) value, which makes them impractical. In this work, we present a \textit{proactive} approach for time-series anomaly detection based on a time-series forecasting model specialized for anomaly detection and a data-driven anomaly detection model. Our proactive approach establishes an anomaly threshold from training data with a data-driven anomaly detection model, and anomalies are subsequently detected by identifying predicted values that exceed the anomaly threshold. In addition, we extensively evaluated the model using four anomaly detection benchmarks and analyzed both predictable and unpredictable anomalies. We attached the source code as supplementary material.

cs.LG↗

arXiv2024

Bayesian Analysis of Spiked Covariance Models: Correcting Eigenvalue Bias and Determining the Number of Spikes

We study Bayesian inference in the spiked covariance model, where a small number of spiked eigenvalues dominate the spectrum. Our goal is to infer the spiked eigenvalues, their corresponding eigenvectors, and the number of spikes, providing a Bayesian solution to principal component analysis with uncertainty quantification. We place an inverse-Wishart prior on the covariance matrix to derive posterior distributions for the spiked eigenvalues and eigenvectors. Although posterior sampling is computationally efficient due to conjugacy, a bias may exist in the posterior eigenvalue estimates under high-dimensional settings. To address this, we propose two bias correction strategies: (i) a hyperparameter adjustment method, and (ii) a post-hoc multiplicative correction. For inferring the number of spikes, we develop a BIC-type approximation to the marginal likelihood and prove posterior consistency in the high-dimensional regime $p>n$. Furthermore, we establish concentration inequalities and posterior contraction rates for the leading eigenstructure, demonstrating minimax optimality for the spiked eigenvector in the single-spike case. Simulation studies and a real data application show that our method performs better than existing approaches in providing accurate quantification of uncertainty for both eigenstructure estimation and estimation of the number of spikes.

math.ST↗

arXiv2024

Formalizing Hyperspaces and Operations on Subsets of Polish Spaces over Abstract Exact Real Numbers

Building on our prior work on axiomatization of exact real computation by formalizing nondeterministic first-order partial computations over real and complex numbers in a constructive dependent type theory, we present a framework for certified computation on hyperspaces of subsets by formalizing various higher-order data types and operations. We first define open, closed, compact and overt subsets for generic spaces in an abstract topological way that allows short and elegant proofs with computational content coinciding with standard definitions in computable analysis and constructive mathematics. From these proofs we can extract programs for testing inclusion, overlapping of sets, et cetera. To enhance the efficiency of the extracted programs, we then focus on Polish spaces, where we give more efficient encodings based on metric properties of the space. As various computational properties depend on the continuity of the encoding functions, we introduce a nondeterministic version of a continuity principle which is natural in our formalization and valid under the standard type-2 realizability interpretation. Using this principle we further derive the computational equivalence between the generic and the metric encodings. Our theory is fully implemented in the Coq proof assistant. From proofs in this Coq formalization, we can extract certified programs for error-free operations on subsets. As an application, we provide a function that constructs fractals in Euclidean space, such as the Sierpinski triangle, from iterated function systems using the limit operation. The resulting programs can be used to draw such fractals up to any desired resolution.

cs.LO↗

arXiv2024

An Imperative Language for Verified Exact Real-Number Computation

We introduce Clerical, a programming language for exact real-number computation that combines first-order imperative-style programming with a limit operator for computation of real numbers as limits of Cauchy sequences. We address the semidecidability of the linear ordering of the reals by incorporating nondeterministic guarded choice, through which decisions based on partial comparison operations on reals can be patched together to give total programs. The interplay between mutable state, nondeterminism, and computation of limits is controlled by the requirement that expressions computing limits and guards modify only local state. We devise a domain-theoretic denotational semantics that uses a variant of Plotkin powerdomain construction tailored to our specific version of nondeterminism. We formulate a Hoare-style specification logic, show that it is sound for the denotational semantics, and illustrate the setup by implementing and proving correct a program for computation of $\pi$ as the least positive zero of $\sin$. The modular character of Clerical allows us to compose the program from smaller parts, each of which is shown to be correct on its own. We provide a proof-of-concept OCaml implementation of Clerical, and formally verify parts of the development, notably the soundness of specification logic, in the Coq proof assistant.

cs.LO↗

arXiv2023

MadSGM: Multivariate Anomaly Detection with Score-based Generative Models

The time-series anomaly detection is one of the most fundamental tasks for time-series. Unlike the time-series forecasting and classification, the time-series anomaly detection typically requires unsupervised (or self-supervised) training since collecting and labeling anomalous observations are difficult. In addition, most existing methods resort to limited forms of anomaly measurements and therefore, it is not clear whether they are optimal in all circumstances. To this end, we present a multivariate time-series anomaly detector based on score-based generative models, called MadSGM, which considers the broadest ever set of anomaly measurement factors: i) reconstruction-based, ii) density-based, and iii) gradient-based anomaly measurements. We also design a conditional score network and its denoising score matching loss for the time-series anomaly detection. Experiments on five real-world benchmark datasets illustrate that MadSGM achieves the most robust and accurate predictions.

cs.LG↗

arXiv2023

Regular Time-series Generation using SGM

Score-based generative models (SGMs) are generative models that are in the spotlight these days. Time-series frequently occurs in our daily life, e.g., stock data, climate data, and so on. Especially, time-series forecasting and classification are popular research topics in the field of machine learning. SGMs are also known for outperforming other generative models. As a result, we apply SGMs to synthesize time-series data by learning conditional score functions. We propose a conditional score network for the time-series generation domain. Furthermore, we also derive the loss function between the score matching and the denoising score matching in the time-series generation domain. Finally, we achieve state-of-the-art results on real-world datasets in terms of sampling diversity and quality.

cs.LG↗

arXiv2022

SOS: Score-based Oversampling for Tabular Data

Score-based generative models (SGMs) are a recent breakthrough in generating fake images. SGMs are known to surpass other generative models, e.g., generative adversarial networks (GANs) and variational autoencoders (VAEs). Being inspired by their big success, in this work, we fully customize them for generating fake tabular data. In particular, we are interested in oversampling minor classes since imbalanced classes frequently lead to sub-optimal training outcomes. To our knowledge, we are the first presenting a score-based tabular data oversampling method. Firstly, we re-design our own score network since we have to process tabular data. Secondly, we propose two options for our generation method: the former is equivalent to a style transfer for tabular data and the latter uses the standard generative policy of SGMs. Lastly, we define a fine-tuning method, which further enhances the oversampling quality. In our experiments with 6 datasets and 10 baselines, our method outperforms other oversampling methods in all cases.

cs.LG↗

arXiv2022

Extracting efficient exact real number computation from proofs in constructive type theory

Exact real computation is an alternative to floating-point arithmetic where operations on real numbers are performed exactly, without the introduction of rounding errors. When proving the correctness of an implementation, one can focus solely on the mathematical properties of the problem without thinking about the subtleties of representing real numbers. We propose a new axiomatization of the real numbers in a dependent type theory with the goal of extracting certified exact real computation programs from constructive proofs. Our formalization differs from similar approaches, in that we formalize the reals in a conceptually similar way as some mature implementations of exact real computation. Primitive operations on reals can be extracted directly to the corresponding operations in such an implementation, producing more efficient programs. We particularly focus on the formalization of partial and nondeterministic computation, which is essential in exact real computation. We prove the soundness of our formalization with regards of the standard realizability interpretation from computable analysis and show how to relate our theory to a classical formalization of the reals. We demonstrate the feasibility of our theory by implementing it in the Coq proof assistant and present several natural examples. From the examples we have automatically extracted Haskell programs that use the exact real computation framework AERN for efficiently performing exact operations on real numbers. In experiments, the extracted programs behave similarly to native implementations in AERN in terms of running time and memory usage.

cs.LO↗

arXiv2021

Multivariate Lévy Adaptive B-Spline Regression

We develop a fully Bayesian nonparametric regression model based on a Lévy process prior named MLABS (Multivariate Lévy Adaptive B-Spline regression) model, a multivariate version of the LARK (Lévy Adaptive Regression Kernels) models, for estimating unknown functions with either varying degrees of smoothness or high interaction orders. Lévy process priors have advantages of encouraging sparsity in the expansions and providing automatic selection over the number of basis functions. The unknown regression function is expressed as a weighted sum of tensor product of B-spline basis functions as the elements of an overcomplete system, which can deal with multi-dimensional data. The B-spline basis can express systematically functions with varying degrees of smoothness. By changing a set of degrees of the tensor product basis function, MLABS can adapt the smoothness of target functions due to the nice properties of B-spline bases. The local support of the B-spline basis enables the MLABS to make more delicate predictions than other existing methods in the two-dimensional surface data. Experiments on various simulated and real-world datasets illustrate that the MLABS model has comparable performance on regression and classification problems. We also show that the MLABS model has more stable and accurate predictive abilities than state-of-the-art nonparametric regression models in relatively low-dimensional data.

stat.CO↗

arXiv2021

Bayesian Nonparametric Classification for Incomplete Data With a High Missing Rate: an Application to Semiconductor Manufacturing Data

During the semiconductor manufacturing process, predicting the yield of the semiconductor is an important problem. Early detection of defective product production in the manufacturing process can save huge production cost. The data generated from the semiconductor manufacturing process have characteristics of highly non-normal distributions, complicated missing patterns and high missing rate, which complicate the prediction of the yield. We propose Dirichlet process - naive Bayes model (DPNB), a classification method based on the mixtures of Dirichlet process and naive Bayes model. Since the DPNB is based on the mixtures of Dirichlet process and learns the joint distribution of all variables involved, it can handle highly non-normal data and can make predictions for the test dataset with any missing patterns. The DPNB also performs well for high missing rates since it uses all information of observed components. Experiments on various real datasets including semiconductor manufacturing data show that the DPNB has better performance than MICE and MissForest in terms of predicting missing values as percentage of missing values increases.

stat.AP↗

arXiv2021

Lévy Adaptive B-spline Regression via Overcomplete Systems

The estimation of functions with varying degrees of smoothness is a challenging problem in the nonparametric function estimation. In this paper, we propose the LABS (Lévy Adaptive B-Spline regression) model, an extension of the LARK models, for the estimation of functions with varying degrees of smoothness. LABS model is a LARK with B-spline bases as generating kernels. The B-spline basis consists of piecewise k degree polynomials with k-1 continuous derivatives and can express systematically functions with varying degrees of smoothness. By changing the orders of the B-spline basis, LABS can systematically adapt the smoothness of functions, i.e., jump discontinuities, sharp peaks, etc. Results of simulation studies and real data examples support that this model catches not only smooth areas but also jumps and sharp peaks of functions. The proposed model also has the best performance in almost all examples. Finally, we provide theoretical results that the mean function for the LABS model belongs to the certain Besov spaces based on the orders of the B-spline basis and that the prior of the model has the full support on the Besov spaces.

stat.ME↗

arXiv2019

Randomized Computation of Continuous Data: Is Brownian Motion Computable?

We consider randomized computation of continuous data in the sense of Computable Analysis. Our first contribution formally confirms that it is no loss of generality to take as sample space the Cantor space of infinite FAIR coin flips. This extends [Schröder&Simpson'05] and [Hoyrup&Rojas'09] considering sequences of suitably and adaptively BIASED coins. Our second contribution is concerned with 1D Brownian Motion (aka Wiener Process), a probability distribution on the space of continuous functions f:[0,1]->R with f(0)=0 whose computability has been conjectured [Davie&Fouché'13; arXiv:1409.4667,S6]. We establish that this (higher-type) random variable is computable iff some/every computable family of moduli of continuity (as ordinary random variables) has a computable probability distribution with respect to the Wiener Measure.

math.NA↗

arXiv2017

Computable Operations on Compact Subsets of Metric Spaces with Applications to Fr\'echet Distance and Shape Optimization

We extend the Theory of Computation on real numbers, continuous real functions, and bounded closed Euclidean subsets, to compact metric spaces $(X,d)$: thereby generically including computational and optimization problems over higher types, such as the compact 'hyper' spaces of (i) nonempty closed subsets of $X$ w.r.t. Hausdorff metric, and of (ii) equicontinuous functions on $X$. The thus obtained Cartesian closure is shown to exhibit the same structural properties as in the Euclidean case, particularly regarding function pre/image. This allows us to assert the computability of (iii) Fr\'echet Distances between curves and between loops, as well as of (iv) constrained/Shape Optimization.

cs.LO↗

arXiv2016

Semantics, Specification Logic, and Hoare Logic of Exact Real Computation

We propose a simple imperative programming language, ERC, that features arbitrary real numbers as primitive data type, exactly. Equipped with a denotational semantics, ERC provides a formal programming language-theoretic foundation to the algorithmic processing of real numbers. In order to capture multi-valuedness, which is well-known to be essential to real number computation, we use a Plotkin powerdomain and make our programming language semantics computable and complete: all and only real functions computable in computable analysis can be realized in ERC. The base programming language supports real arithmetic as well as implicit limits; expansions support additional primitive operations (such as a user-defined exponential function). By restricting integers to Presburger arithmetic and real coercion to the `precision' embedding $\mathbb{Z}\ni p\mapsto 2^p\in\mathbb{R}$, we arrive at a first-order theory which we prove to be decidable and model-complete. Based on said logic as specification language for preconditions and postconditions, we extend Hoare logic to a sound (w.r.t. the denotational semantics) and expressive system for deriving correct total correctness specifications. Various examples demonstrate the practicality and convenience of our language and the extended Hoare logic.

math.NA↗