This paper presents a comprehensive evaluation of three distinct
computational algorithms applied to the decision-making process of real estate
purchases. Specifically, we analyze the efficacy of Linear Regression from
Scikit-learn library, Gaussian Elimination with partial pivoting, and LU
Decomposition in predicting the advisability of buying a house in the State of
Connecticut based on a set of financial and market-related parameters. The
algorithms' performances were compared using a dataset encompassing
town-specific details, yearly data, interest rates, and median sale ratios. Our
results demonstrate significant differences in predictive accuracy, with Linear
Regression and LU Decomposition providing the most reliable recommendations and
Gaussian Elimination showing limitations in stability and performance. The
study's findings emphasize the importance of algorithm selection in predictive
analytic and offer insights into the practical applications of computational
methods in real estate investment strategies. By evaluating model efficacy
through metrics such as R-squared scores and Mean Squared Error, we provide a
nuanced understanding of each method's strengths and weaknesses, contributing
valuable knowledge to the fields of real estate analysis and predictive
modeling.

该研究综合评估了应用于房地产购买决策过程的三种不同的计算算法。结果表明，线性回归和 LU 分解提供了最可靠的建议，而高斯消元则在稳定性和性能方面存在局限性。通过评估模型效能，如 R 平方分数和均方误差等指标，我们对每种方法的优点和缺点有了深入的了解，并为房地产分析和预测建模领域提供了有价值的知识。

CT 房地产购买决策的线性回归、高斯消元法和 LU 分解的比较分析

Comparative Analysis of Linear Regression, Gaussian Elimination, and LU  Decomposition for CT Real Estate Purchase Decisions

A distance matrix $A \in \mathbb R^{n \times m}$ represents all pairwise
distances, $A_{ij}=\mathrm{d}(x_i,y_j)$, between two point sets $x_1,...,x_n$
and $y_1,...,y_m$ in an arbitrary metric space $(\mathcal Z, \mathrm{d})$. Such
matrices arise in various computational contexts such as learning image
manifolds, handwriting recognition, and multi-dimensional unfolding.
In this work we study algorithms for low-rank approximation of distance
matrices. Recent work by Bakshi and Woodruff (NeurIPS 2018) showed it is
possible to compute a rank-$k$ approximation of a distance matrix in time
$O((n+m)^{1+\gamma}) \cdot \mathrm{poly}(k,1/\epsilon)$, where $\epsilon>0$ is
an error parameter and $\gamma>0$ is an arbitrarily small constant. Notably,
their bound is sublinear in the matrix size, which is unachievable for general
matrices.
We present an algorithm that is both simpler and more efficient. It reads
only $O((n+m) k/\epsilon)$ entries of the input matrix, and has a running time
of $O(n+m) \cdot \mathrm{poly}(k,1/\epsilon)$. We complement the sample
complexity of our algorithm with a matching lower bound on the number of
entries that must be read by any algorithm. We provide experimental results to
validate the approximation quality and running time of our algorithm.

本文研究了距离矩阵的低秩近似算法及其样本复杂度，在实验中得到了验证。

距离矩阵的最优低秩逼近

Sample-Optimal Low-Rank Approximation of Distance Matrices

Verifying the correctness of Bayesian computation is challenging. This is
especially true for complex models that are common in practice, as these
require sophisticated model implementations and algorithms. In this paper we
introduce \emph{simulation-based calibration} (SBC), a general procedure for
validating inferences from Bayesian algorithms capable of generating posterior
samples. This procedure not only identifies inaccurate computation and
inconsistencies in model implementations but also provides graphical summaries
that can indicate the nature of the problems that arise. We argue that SBC is a
critical part of a robust Bayesian workflow, as well as being a useful tool for
those developing computational algorithms and statistical software.

介绍了一种名为 “基于模拟的校准（SBC）” 的通用过程，可验证使用贝叶斯算法生成后验样本的推断的正确性和一致性，并提供可指示问题性质的图形总结。

使用基于模拟校准方法验证贝叶斯推断算法

Validating Bayesian Inference Algorithms with Simulation-Based  Calibration

This paper analyzes simultaneous route-and-departure-time (SRDT) dynamic user
equilibrium (DUE) that incorporates the notion of boundedly rational (BR) user
behavior in the selection of departure time and route choices. Intrinsically,
the boundedly rational dynamic user equilibrium (BR-DUE) model we present
assumes that travelers do not always seek the least costly
route-and-departure-time choice. Rather, their perception of travel cost is
affected by an indifference band describing travelers' tolerance of the
difference between their experienced travel costs and the minimum travel cost.
An extension of the BR-DUE problem is the so-called variable tolerance dynamic
user equilibrium (VT-BR-DUE) wherein endogenously determined tolerances may
depend not only on paths, but also on the established path departure rates.
This paper presents a unified approach for modeling both BR-DUE and VT-BR-DUE,
which makes significant contributions to model formulation, analysis of
existence, solution characterization, and heuristic numerical computation of
such problems. The VT-BR-DUE problem, together with the BR-DUE problem as a
special case, is formulated as a variational inequality. We provide a very
general existence result for VT-BR-DUE and BR-DUE that relies on assumptions
weaker than those required for mere DUE models. Moreover, a characterization of
the solution set is provided based on rigorous topological analysis. Finally,
three computational algorithms are proposed based on the VI and DVI
formulations. Numerical studies are conducted to assess the proposed algorithms
in terms of solution quality, convergence, and computational efficiency.

本文提出了一种统一方法来建模同时路线和出发时间动态用户均衡，包括有限理性用户行为概念；我们提供了 VT-BR-DUE 的存在性和解决方案的表征，并提出了基于 VI 和 DVI 公式的三种计算算法，以评估解决方案质量，收敛性和计算效率。