Conjoint analysis is a popular experimental design used to measure multidimensional preferences. Researchers examine how varying a factor of interest, while controlling for other relevant factors, influences decision-making. Currently, there exist two methodological approaches to analyzing data from a conjoint experiment. The first focuses on estimating the average marginal effects of each factor while averaging over the other factors. Although this allows for straightforward design-based estimation, the results critically depend on the distribution of other factors and how interaction effects are aggregated. An alternative model-based approach can compute various quantities of interest, but requires researchers to correctly specify the model, a challenging task for conjoint analysis with many factors and possible interactions. In addition, a commonly used logistic regression has poor statistical properties even with a moderate number of factors when incorporating interactions. We propose a new hypothesis testing approach based on the conditional randomization test to answer the most fundamental question of conjoint analysis: Does a factor of interest matter in any way given the other factors? Our methodology is solely based on the randomization of factors, and hence is free from assumptions. Yet, it allows researchers to use any test statistic, including those based on complex machine learning algorithms. As a result, we are able to combine the strengths of the existing design-based and model-based approaches. We illustrate the proposed methodology through conjoint analysis of immigration preferences and political candidate evaluation. We also extend the proposed approach to test for regularity assumptions commonly used in conjoint analysis.

Group or cluster structure on explanatory variables in machine learning problems is a very general phenomenon, which has attracted broad interest from practitioners and theoreticians alike. In this work we contribute an approach to learning under such group structure, that does not require prior information on the group identities. Our paradigm is motivated by the Laplacian geometry of an underlying network with a related community structure, and proceeds by directly incorporating this into a penalty that is effectively computed via a heat flow-based local network dynamics. In fact, we demonstrate a procedure to construct such a network based on the available data. Notably, we dispense with computationally intensive pre-processing involving clustering of variables, spectral or otherwise. Our technique is underpinned by rigorous theorems that guarantee its effective performance and provide bounds on its sample complexity. In particular, in a wide range of settings, it provably suffices to run the heat flow dynamics for time that is only logarithmic in the problem dimensions. We explore in detail the interfaces of our approach with key statistical physics models in network science, such as the Gaussian Free Field and the Stochastic Block Model. We validate our approach by successful applications to real-world data from a wide array of application domains, including computer science, genetics, climatology and economics. Our work raises the possibility of applying similar diffusion-based techniques to classical learning tasks, exploiting the interplay between geometric, dynamical and stochastic structures underlying the data.

In multivariate time series systems, it has been observed that certain groups of variables partially lead the evolution of the system, while other variables follow this evolution with a time delay; the result is a lead-lag structure amongst the time series variables. In this paper, we propose a method for the detection of lead-lag clusters of time series in multivariate systems. We demonstrate that the web of pairwise lead-lag relationships between time series can be helpfully construed as a directed network, for which there exist suitable algorithms for the detection of pairs of lead-lag clusters with high pairwise imbalance. Within our framework, we consider a number of choices for the pairwise lead-lag metric and directed network clustering components. Our framework is validated on both a synthetic generative model for multivariate lead-lag time series systems and daily real-world US equity prices data. We showcase that our method is able to detect statistically significant lead-lag clusters in the US equity market. We study the nature of these clusters in the context of the empirical finance literature on lead-lag relations and demonstrate how these can be used for the construction of predictive financial signals.

The concept of median/consensus has been widely investigated in order to provide a statistical summary of ranking data, i.e. realizations of a random permutation $\Sigma$ of a finite set, $\{1,\; \ldots,\; n\}$ with $n\geq 1$ say. As it sheds light onto only one aspect of $\Sigma$'s distribution $P$, it may neglect other informative features. It is the purpose of this paper to define analogs of quantiles, ranks and statistical procedures based on such quantities for the analysis of ranking data by means of a metric-based notion of depth function on the symmetric group. Overcoming the absence of vector space structure on $\mathfrak{S}_n$, the latter defines a center-outward ordering of the permutations in the support of $P$ and extends the classic metric-based formulation of consensus ranking (medians corresponding then to the deepest permutations). The axiomatic properties that ranking depths should ideally possess are listed, while computational and generalization issues are studied at length. Beyond the theoretical analysis carried out, the relevance of the novel concepts and methods introduced for a wide variety of statistical tasks are also supported by numerous numerical experiments.

Familiarity with basic statistics and mathematical notation is helpful. An Introduction to Statistical Learning is one of the best introductory textbooks on classical machine learning techniques such as linear regression. It was the first machine learning book I've bought and has given me a great foundation. The explanations are held on a high level, so you don't need advanced math skills. Every chapter comes with code examples and labs in R. It is a great book to work through cover-to-cover. Get "An Introduction to Statistical Learning" on Amazon

In this post, I'll take a look at how you can compare regression models. Comparing regression models is perhaps one of the trickiest tasks to complete in the "comparing models" arena; The reason is that there are literally dozens of statistics you can calculate to compare regression models, including: This list isn't exhaustive–there are many other tools, tests and plots at your disposal. Rather than discuss the statistics in detail, I chose to focus this post on comparing a few of the most popular regression model evaluation techniques and discuss when you might want to use them (or when you might not want to). The techniques listed below tend to be on the "easier to use and understand" end of the spectrum, so if you're new to model comparison it's a good place to start. The first question you should be asking is: How well do I know my data?

Topic taxonomies, which represent the latent topic (or category) structure of document collections, provide valuable knowledge of contents in many applications such as web search and information filtering. Recently, several unsupervised methods have been developed to automatically construct the topic taxonomy from a text corpus, but it is challenging to generate the desired taxonomy without any prior knowledge. In this paper, we study how to leverage the partial (or incomplete) information about the topic structure as guidance to find out the complete topic taxonomy. We propose a novel framework for topic taxonomy completion, named TaxoCom, which recursively expands the topic taxonomy by discovering novel sub-topic clusters of terms and documents. To effectively identify novel topics within a hierarchical topic structure, TaxoCom devises its embedding and clustering techniques to be closely-linked with each other: (i) locally discriminative embedding optimizes the text embedding space to be discriminative among known (i.e., given) sub-topics, and (ii) novelty adaptive clustering assigns terms into either one of the known sub-topics or novel sub-topics. Our comprehensive experiments on two real-world datasets demonstrate that TaxoCom not only generates the high-quality topic taxonomy in terms of term coherency and topic coverage but also outperforms all other baselines for a downstream task.

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in traditional methods. This is because in addition to aleatoric uncertainty associated with noisy data, there is also uncertainty due to limited data, but also due to NN hyperparameters, overparametrization, optimization and sampling errors as well as model misspecification. Although there are some recent works on uncertainty quantification (UQ) in NNs, there is no systematic investigation of suitable methods towards quantifying the total uncertainty effectively and efficiently even for function approximation, and there is even less work on solving partial differential equations and learning operator mappings between infinite-dimensional function spaces using NNs. In this work, we present a comprehensive framework that includes uncertainty modeling, new and existing solution methods, as well as evaluation metrics and post-hoc improvement approaches. To demonstrate the applicability and reliability of our framework, we present an extensive comparative study in which various methods are tested on prototype problems, including problems with mixed input-output data, and stochastic problems in high dimensions. In the Appendix, we include a comprehensive description of all the UQ methods employed, which we will make available as open-source library of all codes included in this framework.

Abstract--The prediction of valence from speech is an important, but challenging problem. The externalization of valence in speech has speaker-dependent cues, which contribute to performances that are often significantly lower than the prediction of other emotional attributes such as arousal and dominance. A practical approach to improve valence prediction from speech is to adapt the models to the target speakers in the test set. Adapting a speech emotion recognition (SER) system to a particular speaker is a hard problem, especially with deep neural networks (DNNs), since it requires optimizing millions of parameters. This study proposes an unsupervised approach to address this problem by searching for speakers in the train set with similar acoustic patterns as the speaker in the test set. Speech samples from the selected speakers are used to create the adaptation set. This approach leverages transfer learning using pre-trained models, which are adapted with these speech samples. We propose three alternative adaptation strategies: unique speaker, oversampling and weighting approaches. These methods differ on the use of the adaptation set in the personalization of the valence models. The results demonstrate that a valence prediction model can be efficiently personalized with these unsupervised approaches, leading to relative improvements as high as 13.52%. Index Terms--Speech emotion recognition, adaptation, transfer learning, emotional dimensions, valence. In potential in fields such as human-computer interactions particular, the emotional attribute valence is key (HCIs), healthcare [1], [2] and behavioral studies to understand many behavioral disorders [6], [7] [3], [4]. Although different is still a challenging task. The usual formulation approaches have been proposed to improve SER to describe emotions is with categorical descriptors systems, the prediction of valence using acoustic such as happiness, sadness, anger and neutral.

Supervised deep learning has shown state-of-the-art performance for medical image segmentation across different applications, including histopathology and cancer research; however, the manual annotation of such data is extremely laborious. In this work, we explore the use of superpixel approaches to compute a pre-segmentation of HER2 stained images for breast cancer diagnosis that facilitates faster manual annotation and correction in a second step. Four methods are compared: Standard Simple Linear Iterative Clustering (SLIC) as a baseline, a domain adapted SLIC, and superpixels based on feature embeddings of a pretrained ResNet-50 and a denoising autoencoder. To tackle oversegmentation, we propose to hierarchically merge superpixels, based on their content in the respective feature space. When evaluating the approaches on fully manually annotated images, we observe that the autoencoder-based superpixels achieve a 23% increase in boundary F1 score compared to the baseline SLIC superpixels. Furthermore, the boundary F1 score increases by 73% when hierarchical clustering is applied on the adapted SLIC and the autoencoder-based superpixels. These evaluations show encouraging first results for a pre-segmentation for efficient manual refinement without the need for an initial set of annotated training data.