We investigate practical algorithms to find or disprove the existence of small subsets of a dataset which, when removed, reverse the sign of a coefficient in an ordinary least squares regression involving that dataset. We empirically study the performance of well-established algorithmic techniques for this task -- mixed integer quadratically constrained optimization for general linear regression problems and exact greedy methods for special cases. We show that these methods largely outperform the state of the art and provide a useful robustness check for regression problems in a few dimensions. However, significant computational bottlenecks remain, especially for the important task of disproving the existence of such small sets of influential samples for regression problems of dimension $3$ or greater. We make some headway on this challenge via a spectral algorithm using ideas drawn from recent innovations in algorithmic robust statistics. We summarize the limitations of known techniques in several challenge datasets to encourage further algorithmic innovation.

Predicting the price of used vehicles is a more interesting and needed problem by many users. Vehicle price prediction can be a challenging task due to the high number of attributes that should be considered for accurate prediction. The major step in the prediction process is the collection and pre-processing of the data. In this project, python scripts were built to normalize, standardize, and clean data to avoid unnecessary noise for machine learning algorithms. The data set used in this project can be very valuable in conducting similar research using different prediction techniques. Many assumptions were made on the basis of the data set. The proposed system uses a Decision tree model and Gradient boosting predictive model, which are combined in other to get closed to accurate prediction, the proposed model was evaluated and it gives a promising performance. The future price prediction of used vehicles with the help of the same data set will comprise different models.

Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for constructing a high-order polynomial regression based on the Taylor map factorization. This method naturally implements multi-target regression and can capture internal relationships between targets. Additionally, we introduce an approach for model interpretation in the form of systems of differential equations. By benchmarking on UCI open access datasets, Feynman symbolic regression datasets, and Friedman-1 datasets, we demonstrate that the proposed method performs comparable to the state-of-the-art regression methods and outperforms them on specific tasks.

Despite tremendous advancements in dialogue systems, stable evaluation still requires human judgments producing notoriously high-variance metrics due to their inherent subjectivity. Moreover, methods and labels in dialogue evaluation are not fully standardized, especially for open-domain chats, with a lack of work to compare and assess the validity of those approaches. The use of inconsistent evaluation can misinform the performance of a dialogue system, which becomes a major hurdle to enhance it. Thus, a dimensional evaluation of chat-oriented open-domain dialogue systems that reliably measures several aspects of dialogue capabilities is desired. This paper presents a novel human evaluation method to estimate the rates of many dialogue system behaviors. Our method is used to evaluate four state-of-the-art open-domain dialogue systems and compared with existing approaches. The analysis demonstrates that our behavior method is more suitable than alternative Likert-style or comparative approaches for dimensional evaluation of these systems.

Conformal prediction is an assumption-lean approach to generating distribution-free prediction intervals or sets, for nearly arbitrary predictive models, with guaranteed finite-sample coverage. Conformal methods are an active research topic in statistics and machine learning, but only recently have they been extended to non-exchangeable data. In this paper, we invite survey methodologists to begin using and contributing to conformal methods. We introduce how conformal prediction can be applied to data from several common complex sample survey designs, under a framework of design-based inference for a finite population, and we point out gaps where survey methodologists could fruitfully apply their expertise. Our simulations empirically bear out the theoretical guarantees of finite-sample coverage, and our real-data example demonstrates how conformal prediction can be applied to complex sample survey data in practice.

Rotational invariance is a popular inductive bias used by many fields in machine learning, such as computer vision and machine learning for quantum chemistry. Rotation-invariant machine learning methods set the state of the art for many tasks, including molecular property prediction and 3D shape classification. These methods generally either rely on task-specific rotation-invariant features, or they use general-purpose deep neural networks which are complicated to design and train. However, it is unclear whether the success of these methods is primarily due to the rotation invariance or the deep neural networks. To address this question, we suggest a simple and general-purpose method for learning rotation-invariant functions of three-dimensional point cloud data using a random features approach. Specifically, we extend the random features method of Rahimi & Recht 2007 by deriving a version that is invariant to three-dimensional rotations and showing that it is fast to evaluate on point cloud data. We show through experiments that our method matches or outperforms the performance of general-purpose rotation-invariant neural networks on standard molecular property prediction benchmark datasets QM7 and QM9. We also show that our method is general-purpose and provides a rotation-invariant baseline on the ModelNet40 shape classification task. Finally, we show that our method has an order of magnitude smaller prediction latency than competing kernel methods.

Algorithmic Gaussianization is a phenomenon that can arise when using randomized sketching or sampling methods to produce smaller representations of large datasets: For certain tasks, these sketched representations have been observed to exhibit many robust performance characteristics that are known to occur when a data sample comes from a sub-gaussian random design, which is a powerful statistical model of data distributions. However, this phenomenon has only been studied for specific tasks and metrics, or by relying on computationally expensive methods. We address this by providing an algorithmic framework for gaussianizing data distributions via averaging, proving that it is possible to efficiently construct data sketches that are nearly indistinguishable (in terms of total variation distance) from sub-gaussian random designs. In particular, relying on a recently introduced sketching technique called Leverage Score Sparsified (LESS) embeddings, we show that one can construct an $n\times d$ sketch of an $N\times d$ matrix $A$, where $n\ll N$, that is nearly indistinguishable from a sub-gaussian design, in time $O(\text{nnz}(A)\log N + nd^2)$, where $\text{nnz}(A)$ is the number of non-zero entries in $A$. As a consequence, strong statistical guarantees and precise asymptotics available for the estimators produced from sub-gaussian designs (e.g., for least squares and Lasso regression, covariance estimation, low-rank approximation, etc.) can be straightforwardly adapted to our sketching framework. We illustrate this with a new approximation guarantee for sketched least squares, among other examples.

Traditional machine learning paradigms are based on the assumption that both training and test data follow the same statistical pattern, which is mathematically referred to as Independent and Identically Distributed ($i.i.d.$). However, in real-world applications, this $i.i.d.$ assumption often fails to hold due to unforeseen distributional shifts, leading to considerable degradation in model performance upon deployment. This observed discrepancy indicates the significance of investigating the Out-of-Distribution (OOD) generalization problem. OOD generalization is an emerging topic of machine learning research that focuses on complex scenarios wherein the distributions of the test data differ from those of the training data. This paper represents the first comprehensive, systematic review of OOD generalization, encompassing a spectrum of aspects from problem definition, methodological development, and evaluation procedures, to the implications and future directions of the field. Our discussion begins with a precise, formal characterization of the OOD generalization problem. Following that, we categorize existing methodologies into three segments: unsupervised representation learning, supervised model learning, and optimization, according to their positions within the overarching learning process. We provide an in-depth discussion on representative methodologies for each category, further elucidating the theoretical links between them. Subsequently, we outline the prevailing benchmark datasets employed in OOD generalization studies. To conclude, we overview the existing body of work in this domain and suggest potential avenues for future research on OOD generalization. A summary of the OOD generalization methodologies surveyed in this paper can be accessed at http://out-of-distribution-generalization.com.

Big data and machine learning tools have jointly empowered humans in making data-driven decisions. However, many of them capture empirical associations that might be spurious due to confounding factors and subgroup heterogeneity. The famous Simpson's paradox is such a phenomenon where aggregated and subgroup-level associations contradict with each other, causing cognitive confusions and difficulty in making adequate interpretations and decisions. Existing tools provide little insights for humans to locate, reason about, and prevent pitfalls of spurious association in practice. We propose VISPUR, a visual analytic system that provides a causal analysis framework and a human-centric workflow for tackling spurious associations. These include a CONFOUNDER DASHBOARD, which can automatically identify possible confounding factors, and a SUBGROUP VIEWER, which allows for the visualization and comparison of diverse subgroup patterns that likely or potentially result in a misinterpretation of causality. Additionally, we propose a REASONING STORYBOARD, which uses a flow-based approach to illustrate paradoxical phenomena, as well as an interactive DECISION DIAGNOSIS panel that helps ensure accountable decision-making. Through an expert interview and a controlled user experiment, our qualitative and quantitative results demonstrate that the proposed "de-paradox" workflow and the designed visual analytic system are effective in helping human users to identify and understand spurious associations, as well as to make accountable causal decisions.

The tree-based ensembles are known for their outstanding performance in classification and regression problems characterized by feature vectors represented by mixed-type variables from various ranges and domains. However, considering regression problems, they are primarily designed to provide deterministic responses or model the uncertainty of the output with Gaussian or parametric distribution. In this work, we introduce TreeFlow, the tree-based approach that combines the benefits of using tree ensembles with the capabilities of modeling flexible probability distributions using normalizing flows. The main idea of the solution is to use a tree-based model as a feature extractor and combine it with a conditional variant of normalizing flow. Consequently, our approach is capable of modeling complex distributions for the regression outputs. We evaluate the proposed method on challenging regression benchmarks with varying volume, feature characteristics, and target dimensionality. We obtain the SOTA results for both probabilistic and deterministic metrics on datasets with multi-modal target distributions and competitive results on unimodal ones compared to tree-based regression baselines.