Graduate School of Information Science and Technology Osaka University Osaka, Japan thanasutives@ai.sanken.osaka-u.ac.jp Ken-ichi Fukui SANKEN (The Institute of Scientific and Industrial Research) Osaka University Osaka, Japan fukui@ai.sanken.osaka-u.ac.jp The uncertainty-penalized information criterion (UBIC) has been proposed as a new model-selection criterion for data-driven partial differential equation (PDE) discovery. In this paper, we show that using the UBIC is equivalent to employing the conventional BIC to a set of overparameterized models derived from the potential regression models of different complexity measures. The result indicates that the asymptotic property of the UBIC and BIC holds indifferently.

Survival regression aims to predict the time when an event of interest will take place, typically a death or a failure. A fully parametric method [18] is proposed to estimate the survival function as a mixture of individual parametric distributions in the presence of censoring. In this paper, We present a novel method to predict the survival time by better clustering the survival data and combine primitive distributions. We propose two variants of variational auto-encoder (VAE), discrete and continuous, to generate the latent variables for clustering input covariates. The model is trained end to end by jointly optimizing the VAE loss and regression loss. Thorough experiments on dataset SUPPORT and FLCHAIN show that our method can effectively improve the clustering result and reach competitive scores with previous methods. We demonstrate the superior result of our model prediction in the long-term. Our code is available at https://github.com/

We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix. All prior private algorithms for this task require either $d^{3/2}$ examples, error growing polynomially with the condition number, or exponential time. Our near-optimal accuracy guarantee holds for any dataset with bounded statistical leverage and bounded residuals. Technically, we build on the approach of Brown et al. (2023) for private mean estimation, adding scaled noise to a carefully designed stable nonprivate estimator of the empirical regression vector.

We show that, for finite-sum minimization problems, incorporating partial second-order information of the objective function can dramatically improve the robustness to mini-batch size of variance-reduced stochastic gradient methods, making them more scalable while retaining their benefits over traditional Newton-type approaches. We demonstrate this phenomenon on a prototypical stochastic second-order algorithm, called Mini-Batch Stochastic Variance-Reduced Newton ($\texttt{Mb-SVRN}$), which combines variance-reduced gradient estimates with access to an approximate Hessian oracle. In particular, we show that when the data size $n$ is sufficiently large, i.e., $n\gg \alpha^2\kappa$, where $\kappa$ is the condition number and $\alpha$ is the Hessian approximation factor, then $\texttt{Mb-SVRN}$ achieves a fast linear convergence rate that is independent of the gradient mini-batch size $b$, as long $b$ is in the range between $1$ and $b_{\max}=O(n/(\alpha \log n))$. Only after increasing the mini-batch size past this critical point $b_{\max}$, the method begins to transition into a standard Newton-type algorithm which is much more sensitive to the Hessian approximation quality. We demonstrate this phenomenon empirically on benchmark optimization tasks showing that, after tuning the step size, the convergence rate of $\texttt{Mb-SVRN}$ remains fast for a wide range of mini-batch sizes, and the dependence of the phase transition point $b_{\max}$ on the Hessian approximation factor $\alpha$ aligns with our theoretical predictions.

Differential equations are pivotal in modeling and understanding the dynamics of various systems, offering insights into their future states through parameter estimation fitted to time series data. In fields such as economy, politics, and biology, the observation data points in the time series are often independently obtained (i.e., Repeated Cross-Sectional (RCS) data). With RCS data, we found that traditional methods for parameter estimation in differential equations, such as using mean values of time trajectories or Gaussian Process-based trajectory generation, have limitations in estimating the shape of parameter distributions, often leading to a significant loss of data information. To address this issue, we introduce a novel method, Estimation of Parameter Distribution (EPD), providing accurate distribution of parameters without loss of data information. EPD operates in three main steps: generating synthetic time trajectories by randomly selecting observed values at each time point, estimating parameters of a differential equation that minimize the discrepancy between these trajectories and the true solution of the equation, and selecting the parameters depending on the scale of discrepancy. We then evaluated the performance of EPD across several models, including exponential growth, logistic population models, and target celllimited models with delayed virus production, demonstrating its superiority in capturing the shape of parameter distributions. Furthermore, we applied EPD to real-world datasets, capturing various shapes of parameter distributions rather than a normal distribution. These results effectively address the heterogeneity within systems, marking a substantial progression in accurately modeling systems using RCS data. Thus, EPD marks a significant advancement in accurately modeling systems with RCS data, enabling a deeper understanding of system dynamics and parameter variability.

We present a novel and flexible framework for localized tuning of Hamiltonian Monte Carlo samplers by sampling the algorithm's tuning parameters conditionally based on the position and momentum at each step. For adaptively sampling path lengths, we show that randomized Hamiltonian Monte Carlo, the No-U-Turn Sampler, and the Apogee-to-Apogee Path Sampler all fit within this unified framework as special cases. The framework is illustrated with a simple alternative to the No-U-Turn Sampler for locally adapting path lengths.

The data-driven newsvendor problem with features has recently emerged as a significant area of research, driven by the proliferation of data across various sectors such as retail, supply chains, e-commerce, and healthcare. Given the sensitive nature of customer or organizational data often used in feature-based analysis, it is crucial to ensure individual privacy to uphold trust and confidence. Despite its importance, privacy preservation in the context of inventory planning remains unexplored. A key challenge is the nonsmoothness of the newsvendor loss function, which sets it apart from existing work on privacy-preserving algorithms in other settings. This paper introduces a novel approach to estimate a privacy-preserving optimal inventory policy within the f-differential privacy framework, an extension of the classical $(\epsilon, \delta)$-differential privacy with several appealing properties. We develop a clipped noisy gradient descent algorithm based on convolution smoothing for optimal inventory estimation to simultaneously address three main challenges: (1) unknown demand distribution and nonsmooth loss function; (2) provable privacy guarantees for individual-level data; and (3) desirable statistical precision. We derive finite-sample high-probability bounds for optimal policy parameter estimation and regret analysis. By leveraging the structure of the newsvendor problem, we attain a faster excess population risk bound compared to that obtained from an indiscriminate application of existing results for general nonsmooth convex loss. Our bound aligns with that for strongly convex and smooth loss function. Our numerical experiments demonstrate that the proposed new method can achieve desirable privacy protection with a marginal increase in cost.

Surrogate models provide a quick-to-evaluate approximation to complex computational models and are essential for multi-query problems like design optimisation. The inputs of current computational models are usually high-dimensional and uncertain. We consider Bayesian inference for constructing statistical surrogates with input uncertainties and intrinsic dimensionality reduction. The surrogates are trained by fitting to data from prevalent deterministic computational models. The assumed prior probability density of the surrogate is a Gaussian process. We determine the respective posterior probability density and parameters of the posited statistical model using variational Bayes. The non-Gaussian posterior is approximated by a simpler trial density with free variational parameters and the discrepancy between them is measured using the Kullback-Leibler (KL) divergence. We employ the stochastic gradient method to compute the variational parameters and other statistical model parameters by minimising the KL divergence. We demonstrate the accuracy and versatility of the proposed reduced dimension variational Gaussian process (RDVGP) surrogate on illustrative and robust structural optimisation problems with cost functions depending on a weighted sum of the mean and standard deviation of model outputs.

We are witnessing an increasing availability of streaming data that may contain valuable information on the underlying processes. It is thus attractive to be able to deploy machine learning models on edge devices near sensors such that decisions can be made instantaneously, rather than first having to transmit incoming data to servers. To enable deployment on edge devices with limited storage and computational capabilities, the full-precision parameters in standard models can be quantized to use fewer bits. The resulting quantized models are then calibrated using back-propagation and full training data to ensure accuracy. This one-time calibration works for deployments in static environments. However, model deployment in dynamic edge environments call for continual calibration to adaptively adjust quantized models to fit new incoming data, which may have different distributions. The first difficulty in enabling continual calibration on the edge is that the full training data may be too large and thus not always available on edge devices. The second difficulty is that the use of back-propagation on the edge for repeated calibration is too expensive. We propose QCore to enable continual calibration on the edge. First, it compresses the full training data into a small subset to enable effective calibration of quantized models with different bit-widths. We also propose means of updating the subset when new streaming data arrives to reflect changes in the environment, while not forgetting earlier training data. Second, we propose a small bit-flipping network that works with the subset to update quantized model parameters, thus enabling efficient continual calibration without back-propagation. An experimental study, conducted with real-world data in a continual learning setting, offers insight into the properties of QCore and shows that it is capable of outperforming strong baseline methods.

Large Language Models (LLMs) have experienced widespread adoption across scientific and industrial domains due to their versatility and utility for diverse tasks. Nevertheless, deploying and serving these models at scale with optimal throughput and latency remains a significant challenge, primarily because of the high computational and memory demands associated with LLMs. To tackle this limitation, we introduce Expert Router, a system designed to orchestrate multiple expert models efficiently, thereby enhancing scalability. Expert Router is a parallel inference system with a central routing gateway that distributes incoming requests using a clustering method. This approach effectively partitions incoming requests among available LLMs, maximizing overall throughput. Our extensive evaluations encompassed up to 1,000 concurrent users, providing comprehensive insights into the system's behavior from user and infrastructure perspectives. The results demonstrate Expert Router's effectiveness in handling high-load scenarios and achieving higher throughput rates, particularly under many concurrent users.