In Bayesian inference, a simple and popular approach to reduce the burden of computing high dimensional integrals against a posterior $\pi$ is to make the Laplace approximation $\hat\gamma$. This is a Gaussian distribution, so computing $\int fd\pi$ via the approximation $\int fd\hat\gamma$ is significantly less expensive. In this paper, we make two general contributions to the topic of high-dimensional Laplace approximations, as well as a third contribution specific to a logistic regression model. First, we tighten the dimension dependence of the error $|\int fd\pi - \int fd\hat\gamma|$ for a broad class of functions $f$. Second, we derive a higher-accuracy approximation $\hat\gamma_S$ to $\pi$, which is a skew-adjusted modification to $\hat\gamma$. Our third contribution - in the setting of Bayesian inference for logistic regression with Gaussian design - is to use the first two results to derive upper bounds which hold uniformly over different sample realizations, and lower bounds on the Laplace mean approximation error. In particular, we prove a skewed Bernstein-von Mises Theorem in this logistic regression setting.
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Recently, advancements in deep learning-based superpixel segmentation methods have brought about improvements in both the efficiency and the performance of segmentation. However, a significant challenge remains in generating superpixels that strictly adhere to object boundaries while conveying rich visual significance, especially when cross-surface color correlations may interfere with objects. Drawing inspiration from neural structure and visual mechanisms, we propose a biological network architecture comprising an Enhanced Screening Module (ESM) and a novel Boundary-Aware Label (BAL) for superpixel segmentation. The ESM enhances semantic information by simulating the interactive projection mechanisms of the visual cortex. Additionally, the BAL emulates the spatial frequency characteristics of visual cortical cells to facilitate the generation of superpixels with strong boundary adherence. We demonstrate the effectiveness of our approach through evaluations on both the BSDS500 dataset and the NYUv2 dataset.
Recently, Sato et al. proposed an public verifiable blind quantum computation (BQC) protocol by inserting a third-party arbiter. However, it is not true public verifiable in a sense, because the arbiter is determined in advance and participates in the whole process. In this paper, a public verifiable protocol for measurement-only BQC is proposed. The fidelity between arbitrary states and the graph states of 2-colorable graphs is estimated by measuring the entanglement witnesses of the graph states,so as to verify the correctness of the prepared graph states. Compared with the previous protocol, our protocol is public verifiable in the true sense by allowing other random clients to execute the public verification. It also has greater advantages in the efficiency, where the number of local measurements is O(n^3*log {n}) and graph states' copies is O(n^2*log{n}).
Conditional independence plays a foundational role in database theory, probability theory, information theory, and graphical models. In databases, conditional independence appears in database normalization and is known as the (embedded) multivalued dependency. Many properties of conditional independence are shared across various domains, and to some extent these commonalities can be studied through a measure-theoretic approach. The present paper proposes an alternative approach via semiring relations, defined by extending database relations with tuple annotations from some commutative semiring. Integrating various interpretations of conditional independence in this context, we investigate how the choice of the underlying semiring impacts the corresponding axiomatic and decomposition properties. We specifically identify positivity and multiplicative cancellativity as the key semiring properties that enable extending results from the relational context to the broader semiring framework. Additionally, we explore the relationships between different conditional independence notions through model theory, and consider how methods to test logical consequence and validity generalize from database theory and information theory to semiring relations.
We extend the recently introduced setting of coherent differentiation for taking into account not only differentiation, but also Taylor expansion in categories which are not necessarily (left)additive.The main idea consists in extending summability into an infinitary functor which intuitively maps any object to the object of its countable summable families.This functor is endowed with a canonical structure of bimonad.In a linear logical categorical setting, Taylor expansion is then axiomatized as a distributive law between this summability functor and the resource comonad (aka.~exponential), allowing to extend the summability functor into a bimonad on the Kleisli category of the resource comonad: this extended functor computes the Taylor expansion of the (nonlinear) morphisms of the Kleisli category.We also show how this categorical axiomatizations of Taylor expansion can be generalized to arbitrary cartesian categories, leading to a general theory of Taylor expansion formally similar to that of differential cartesian categories, although it does not require the underlying cartesian category to be left additive.We provide several examples of concrete categories which arise in denotational semantics and feature such analytic structures.
Sewer pipe network systems are an important part of civil infrastructure, and in order to find a good trade-off between maintenance costs and system performance, reliable sewer pipe degradation models are essential. In this paper, we present a large-scale case study in the city of Breda in the Netherlands. Our dataset has information on sewer pipes built since the 1920s and contains information on different covariates. We also have several types of damage, but we focus our attention on infiltrations, surface damage, and cracks. Each damage has an associated severity index ranging from 1 to 5. To account for the characteristics of sewer pipes, we defined 6 cohorts of interest. Two types of discrete-time Markov chains (DTMC), which we called Chain `Multi' and `Single' (where Chain `Multi' contains additional transitions compared to Chain `Single'), are commonly used to model sewer pipe degradation at the pipeline level, and we want to evaluate which suits better our case study. To calibrate the DTMCs, we define an optimization process using Sequential Least-Squares Programming to find the DTMC parameter that best minimizes the root mean weighted square error. Our results show that for our case study, there is no substantial difference between Chain `Multi' and `Single', but the latter has fewer parameters and can be easily trained. Our DTMCs are useful to compare the cohorts via the expected values, e.g., concrete pipes carrying mixed and waste content reach severe levels of surface damage more quickly compared to concrete pipes carrying rainwater, which is a phenomenon typically identified in practice.
Hindsight Experience Replay (HER) is a technique used in reinforcement learning (RL) that has proven to be very efficient for training off-policy RL-based agents to solve goal-based robotic manipulation tasks using sparse rewards. Even though HER improves the sample efficiency of RL-based agents by learning from mistakes made in past experiences, it does not provide any guidance while exploring the environment. This leads to very large training times due to the volume of experience required to train an agent using this replay strategy. In this paper, we propose a method that uses primitive behaviours that have been previously learned to solve simple tasks in order to guide the agent toward more rewarding actions during exploration while learning other more complex tasks. This guidance, however, is not executed by a manually designed curriculum, but rather using a critic network to decide at each timestep whether or not to use the actions proposed by the previously-learned primitive policies. We evaluate our method by comparing its performance against HER and other more efficient variations of this algorithm in several block manipulation tasks. We demonstrate the agents can learn a successful policy faster when using our proposed method, both in terms of sample efficiency and computation time. Code is available at //github.com/franroldans/qmp-her.
Generalized cross-validation (GCV) is a widely-used method for estimating the squared out-of-sample prediction risk that employs a scalar degrees of freedom adjustment (in a multiplicative sense) to the squared training error. In this paper, we examine the consistency of GCV for estimating the prediction risk of arbitrary ensembles of penalized least squares estimators. We show that GCV is inconsistent for any finite ensemble of size greater than one. Towards repairing this shortcoming, we identify a correction that involves an additional scalar correction (in an additive sense) based on degrees of freedom adjusted training errors from each ensemble component. The proposed estimator (termed CGCV) maintains the computational advantages of GCV and requires neither sample splitting, model refitting, or out-of-bag risk estimation. The estimator stems from a finer inspection of ensemble risk decomposition and two intermediate risk estimators for the components in this decomposition. We provide a non-asymptotic analysis of the CGCV and the two intermediate risk estimators for ensembles of convex penalized estimators under Gaussian features and a linear response model. In the special case of ridge regression, we extend the analysis to general feature and response distributions using random matrix theory, which establishes model-free uniform consistency of CGCV.
Graphics Processing Unit, or GPUs, have been successfully adopted both for graphic computation in 3D applications, and for general purpose application (GP-GPUs), thank to their tremendous performance-per-watt. Recently, there is a big interest in adopting them also within automotive and avionic industrial settings, imposing for the first time real-time constraints on the design of such devices. Unfortunately, it is extremely hard to extract timing guarantees from modern GPU designs, and current approaches rely on a model where the GPU is treated as a unique monolithic execution device. Unlike state-of-the-art of research, we try to open the box of modern GPU architectures, providing a clean way to exploit intra-GPU predictable execution.
Contemporary Ghanaian popular singing combines European and traditional Ghanaian influences. We hypothesize that access to technology embedded with equal temperament catalyzed a progressive alignment of Ghanaian singing with equal-tempered scales over time. To test this, we study the Ghanaian singer Daddy Lumba, whose work spans from the earliest Ghanaian electronic style in the late 1980s to the present. Studying a singular musician as a case study allows us to refine our analysis without over-interpreting the findings. We curated a collection of his songs, distributed between 1989 and 2016, to extract F0 values from isolated vocals. We used Gaussian mixture modeling (GMM) to approximate each song's scale and found that the pitch variance has been decreasing over time. We also determined whether the GMM components follow the arithmetic relationships observed in equal-tempered scales, and observed that Daddy Lumba's singing better aligns with equal temperament in recent years. Together, results reveal the impact of exposure to equal-tempered scales, resulting in lessened microtonal content in Daddy Lumba's singing. Our study highlights a potential vulnerability of Ghanaian musical scales and implies a need for research that maps and archives singing styles.
This paper concerns about the limiting distributions of change point estimators, in a high-dimensional linear regression time series context, where a regression object $(y_t, X_t) \in \mathbb{R} \times \mathbb{R}^p$ is observed at every time point $t \in \{1, \ldots, n\}$. At unknown time points, called change points, the regression coefficients change, with the jump sizes measured in $\ell_2$-norm. We provide limiting distributions of the change point estimators in the regimes where the minimal jump size vanishes and where it remains a constant. We allow for both the covariate and noise sequences to be temporally dependent, in the functional dependence framework, which is the first time seen in the change point inference literature. We show that a block-type long-run variance estimator is consistent under the functional dependence, which facilitates the practical implementation of our derived limiting distributions. We also present a few important byproducts of our analysis, which are of their own interest. These include a novel variant of the dynamic programming algorithm to boost the computational efficiency, consistent change point localisation rates under temporal dependence and a new Bernstein inequality for data possessing functional dependence. Extensive numerical results are provided to support our theoretical results. The proposed methods are implemented in the R package \texttt{changepoints} \citep{changepoints_R}.
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