Coupled matrix and tensor factorizations (CMTF) have emerged as an effective data fusion tool to jointly analyze data sets in the form of matrices and higher-order tensors. The PARAFAC2 model has shown to be a promising alternative to the CANDECOMP/PARAFAC (CP) tensor model due to its flexibility and capability to handle irregular/ragged tensors. While fusion models based on a PARAFAC2 model coupled with matrix/tensor decompositions have been recently studied, they are limited in terms of possible regularizations and/or types of coupling between data sets. In this paper, we propose an algorithmic framework for fitting PARAFAC2-based CMTF models with the possibility of imposing various constraints on all modes and linear couplings, using Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). Through numerical experiments, we demonstrate that the proposed algorithmic approach accurately recovers the underlying patterns using various constraints and linear couplings.

Many applications in computational sciences and statistical inference require the computation of expectations with respect to complex high-dimensional distributions with unknown normalization constants, as well as the estimation of these constants. Here we develop a method to perform these calculations based on generating samples from a simple base distribution, transporting them by the flow generated by a velocity field, and performing averages along these flowlines. This non-equilibrium importance sampling (NEIS) strategy is straightforward to implement and can be used for calculations with arbitrary target distributions. On the theory side, we discuss how to tailor the velocity field to the target and establish general conditions under which the proposed estimator is a perfect estimator with zero-variance. We also draw connections between NEIS and approaches based on mapping a base distribution onto a target via a transport map. On the computational side, we show how to use deep learning to represent the velocity field by a neural network and train it towards the zero variance optimum. These results are illustrated numerically on benchmark examples (with dimension up to $10$), where after training the velocity field, the variance of the NEIS estimator is reduced by up to $6$ orders of magnitude than that of a vanilla estimator. We also compare the performances of NEIS with those of Neal's annealed importance sampling (AIS).

Adults with mild-to-moderate hearing loss can use over-the-counter hearing aids to treat their hearing loss at a fraction of traditional hearing care costs. These products incorporate self-fitting methods that allow end-users to configure their hearing aids without the help of an audiologist. A self-fitting method helps users configure the gain-frequency responses that control the amplification for each frequency band of the incoming sound. This paper considers how to design effective self-fitting methods and whether we may evaluate certain aspects of their design without resorting to expensive user studies. Most existing fitting methods provide various user interfaces to allow users to select a configuration from a predetermined set of presets. We propose a novel metric for evaluating the performance of preset-based approaches by computing their population coverage. The population coverage estimates the fraction of users for which it is possible to find a configuration they prefer. A unique aspect of our approach is a probabilistic model that captures how a user's unique preferences differ from other users with similar hearing loss. Next, we develop methods for determining presets to maximize population coverage. Exploratory results demonstrate that the proposed algorithms can effectively select a small number of presets that provide higher population coverage than clustering-based approaches. Moreover, we may use our algorithms to configure the number of increments for slider-based methods.

More than twenty years after its introduction, Annealed Importance Sampling (AIS) remains one of the most effective methods for marginal likelihood estimation. It relies on a sequence of distributions interpolating between a tractable initial distribution and the target distribution of interest which we simulate from approximately using a non-homogeneous Markov chain. To obtain an importance sampling estimate of the marginal likelihood, AIS introduces an extended target distribution to reweight the Markov chain proposal. While much effort has been devoted to improving the proposal distribution used by AIS, an underappreciated issue is that AIS uses a convenient but suboptimal extended target distribution. We here leverage recent progress in score-based generative modeling (SGM) to approximate the optimal extended target distribution minimizing the variance of the marginal likelihood estimate for AIS proposals corresponding to the discretization of Langevin and Hamiltonian dynamics. We demonstrate these novel, differentiable, AIS procedures on a number of synthetic benchmark distributions and variational auto-encoders.

We introduce the first automated models for classifying natural language descriptions provided in cost documents called "Bills of Quantities" (BoQs) popular in the infrastructure construction industry, into the International Construction Measurement Standard (ICMS). The models we deployed and systematically evaluated for multi-class text classification are learnt from a dataset of more than 50 thousand descriptions of items retrieved from 24 large infrastructure construction projects across the United Kingdom. We describe our approach to language representation and subsequent modelling to examine the strength of contextual semantics and temporal dependency of language used in construction project documentation. To do that we evaluate two experimental pipelines to inferring ICMS codes from text, on the basis of two different language representation models and a range of state-of-the-art sequence-based classification methods, including recurrent and convolutional neural network architectures. The findings indicate a highly effective and accurate ICMS automation model is within reach, with reported accuracy results above 90% F1 score on average, on 32 ICMS categories. Furthermore, due to the specific nature of language use in the BoQs text; short, largely descriptive and technical, we find that simpler models compare favourably to achieving higher accuracy results. Our analysis suggest that information is more likely embedded in local key features in the descriptive text, which explains why a simpler generic temporal convolutional network (TCN) exhibits comparable memory to recurrent architectures with the same capacity, and subsequently outperforms these at this task.

Domain adaptation arises as an important problem in statistical learning theory when the data-generating processes differ between training and test samples, respectively called source and target domains. Recent theoretical advances show that the success of domain adaptation algorithms heavily relies on their ability to minimize the divergence between the probability distributions of the source and target domains. However, minimizing this divergence cannot be done independently of the minimization of other key ingredients such as the source risk or the combined error of the ideal joint hypothesis. The trade-off between these terms is often ensured by algorithmic solutions that remain implicit and not directly reflected by the theoretical guarantees. To get to the bottom of this issue, we propose in this paper a new theoretical framework for domain adaptation through hierarchical optimal transport. This framework provides more explicit generalization bounds and allows us to consider the natural hierarchical organization of samples in both domains into classes or clusters. Additionally, we provide a new divergence measure between the source and target domains called Hierarchical Wasserstein distance that indicates under mild assumptions, which structures have to be aligned to lead to a successful adaptation.

Dimension reduction and data visualization aim to project a high-dimensional dataset to a low-dimensional space while capturing the intrinsic structures in the data. It is an indispensable part of modern data science, and many dimensional reduction and visualization algorithms have been developed. However, different algorithms have their own strengths and weaknesses, making it critically important to evaluate their relative performance for a given dataset, and to leverage and combine their individual strengths. In this paper, we propose an efficient spectral method for assessing and combining multiple visualizations of a given dataset produced by diverse algorithms. The proposed method provides a quantitative measure -- the visualization eigenscore -- of the relative performance of the visualizations for preserving the structure around each data point. Then it leverages the eigenscores to obtain a consensus visualization, which has much improved { quality over the individual visualizations in capturing the underlying true data structure.} Our approach is flexible and works as a wrapper around any visualizations. We analyze multiple simulated and real-world datasets from diverse applications to demonstrate the effectiveness of the eigenscores for evaluating visualizations and the superiority of the proposed consensus visualization. Furthermore, we establish rigorous theoretical justification of our method based on a general statistical framework, yielding fundamental principles behind the empirical success of consensus visualization along with practical guidance.

Recovering linear subspaces from data is a fundamental and important task in statistics and machine learning. Motivated by heterogeneity in Federated Learning settings, we study a basic formulation of this problem: the principal component analysis (PCA), with a focus on dealing with irregular noise. Our data come from $n$ users with user $i$ contributing data samples from a $d$-dimensional distribution with mean $\mu_i$. Our goal is to recover the linear subspace shared by $\mu_1,\ldots,\mu_n$ using the data points from all users, where every data point from user $i$ is formed by adding an independent mean-zero noise vector to $\mu_i$. If we only have one data point from every user, subspace recovery is information-theoretically impossible when the covariance matrices of the noise vectors can be non-spherical, necessitating additional restrictive assumptions in previous work. We avoid these assumptions by leveraging at least two data points from each user, which allows us to design an efficiently-computable estimator under non-spherical and user-dependent noise. We prove an upper bound for the estimation error of our estimator in general scenarios where the number of data points and amount of noise can vary across users, and prove an information-theoretic error lower bound that not only matches the upper bound up to a constant factor, but also holds even for spherical Gaussian noise. This implies that our estimator does not introduce additional estimation error (up to a constant factor) due to irregularity in the noise. We show additional results for a linear regression problem in a similar setup.

The satisfiability problem is one of the most famous problems in computer science. Its NP-completeness has been used to argue that SAT is intractable. However, there have been tremendous advances that allow SAT solvers to solve instances with millions of variables. A particularly successful paradigm is stochastic local search. In most cases, there are different ways of formulating the underlying problem. While it is known that this has an impact on the runtime of solvers, finding a helpful formulation is generally non-trivial. The recently introduced GapSAT solver [Lorenz and W\"orz 2020] demonstrated a successful way to improve the performance of an SLS solver on average by learning additional information which logically entails from the original problem. Still, there were cases in which the performance slightly deteriorated. This justifies in-depth investigations into how learning logical implications affects runtimes for SLS. In this work, we propose a method for generating logically equivalent problem formulations, generalizing the ideas of GapSAT. This allows a rigorous mathematical study of the effect on the runtime of SLS solvers. If the modification process is treated as random, Johnson SB distributions provide a perfect characterization of the hardness. Since the observed Johnson SB distributions approach lognormal distributions, our analysis also suggests that the hardness is long-tailed. As a second contribution, we theoretically prove that restarts are useful for long-tailed distributions. This implies that additional restarts can further refine all algorithms employing above mentioned modification technique. Since the empirical studies compellingly suggest that the runtime distributions follow Johnson SB distributions, we investigate this property theoretically. We succeed in proving that the runtimes for Sch\"oning's random walk algorithm are approximately Johnson SB.

A critical element in the development and deployment of AVs is the design of car-following (CF) controllers capable of producing desirable performance in real-world settings. Ideally, a CF control system would effectively and safely handle the longitudinal maneuvers of the vehicle at every encounter it faces. However, designing and training such a controller requires enormous data, testing, and experimentation that covers all possible driving scenarios/encounters. In other words, it requires us to have a perfect understanding of the environment these AVs would be operating under. Clearly, this is very challenging and, possibly, unattainable. AVs are likely to encounter unseen scenarios and be exposed to exogenous and endogenous uncertainties in the physical world. The sources of exogenous and endogenous uncertainties are vast and roughly classified into (Macfarlane and Stroila, 2016; Yao et al., 2020; Katrakazas et al., 2015): (i) vehicular and system dynamics (e.g., vehicle condition, road gradient, aerodynamic drag force, external loads, transmission, brake, the performance of the engine, etc.), (ii) environmental conditions (snow, dust, wind, wet conditions, etc.), and (iii) situational detection (e.g., sensor/measurement errors, radar errors, vehicle speed fluctuations, vehicle localization, communication latency, etc.). All these types of uncertainties can hinder desirable performance (e.g., stability). Yet, a major challenge lies in the complexity of integrating these uncertainties into the control system and the design of the AV.