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Michael Eichler

Publications and source records attributed to Michael Eichler.

12 recordsLinked to original sources
arXiv2023

MetRoBERTa: Leveraging Traditional Customer Relationship Management Data to Develop a Transit-Topic-Aware Language Model

Transit riders' feedback provided in ridership surveys, customer relationship management (CRM) channels, and in more recent times, through social media is key for transit agencies to better gauge the efficacy of their services and initiatives. Getting a holistic understanding of riders' experience through the feedback shared in those instruments is often challenging, mostly due to the open-ended, unstructured nature of text feedback. In this paper, we propose leveraging traditional transit CRM feedback to develop and deploy a transit-topic-aware large language model (LLM) capable of classifying open-ended text feedback to relevant transit-specific topics. First, we utilize semi-supervised learning to engineer a training dataset of 11 broad transit topics detected in a corpus of 6 years of customer feedback provided to the Washington Metropolitan Area Transit Authority (WMATA). We then use this dataset to train and thoroughly evaluate a language model based on the RoBERTa architecture. We compare our LLM, MetRoBERTa, to classical machine learning approaches utilizing keyword-based and lexicon representations. Our model outperforms those methods across all evaluation metrics, providing an average topic classification accuracy of 90%. Finally, we provide a value proposition of this work demonstrating how the language model, alongside additional text processing tools, can be applied to add structure to open-ended text sources of feedback like Twitter. The framework and results we present provide a pathway for an automated, generalizable approach for ingesting, visualizing, and reporting transit riders' feedback at scale, enabling agencies to better understand and improve customer experience.

cs.AI↗
arXiv2019

A note on Herglotz's theorem for time series on function spaces

In this article, we prove Herglotz's theorem for Hilbert-valued time series. This requires the notion of an operator-valued measure, which we shall make precise for our setting. Herglotz's theorem for functional time series allows to generalize existing results that are central to frequency domain analysis on the function space. In particular, we use this result to prove the existence of a functional Cram{é}r representation of a large class of processes, including those with jumps in the spectral distribution and long-memory processes. We furthermore obtain an optimal finite dimensional reduction of the time series under weaker assumptions than available in the literature. The results of this paper therefore enable Fourier analysis for processes of which the spectral density operator does not necessarily exist.

math.ST↗
arXiv2018

Data-adaptive estimation of time-varying spectral densities

This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The performance of these nonparametric estimators, however, depends crucially on the smoothing bandwidths that need to be specified in both time and frequency direction. As an alternative and extension to traditional bandwidth selection methods, we propose an iterative algorithm for constructing localized smoothing kernels data-adaptively. The main idea, inspired by the concept of propagation-separation (Polzehl and Spokoiny 2006), is to determine for a point in the time-frequency plane the largest local vicinity over which smoothing is justified by the data. By shaping the smoothing kernels nonparametrically, our method not only avoids the problem of bandwidth selection in the strict sense but also becomes more flexible. It not only adapts to changing curvature in smoothly varying spectra but also adjusts for structural breaks in the time-varying spectrum.

stat.CO↗
arXiv2017

Locally Stationary Functional Time Series

The literature on time series of functional data has focused on processes of which the probabilistic law is either constant over time or constant up to its second-order structure. Especially for long stretches of data it is desirable to be able to weaken this assumption. This paper introduces a framework that will enable meaningful statistical inference of functional data of which the dynamics change over time. We put forward the concept of local stationarity in the functional setting and establish a class of processes that have a functional time-varying spectral representation. Subsequently, we derive conditions that allow for fundamental results from nonstationary multivariate time series to carry over to the function space. In particular, time-varying functional ARMA processes are investigated and shown to be functional locally stationary according to the proposed definition. As a side-result, we establish a Cramér representation for an important class of weakly stationary functional processes. Important in our context is the notion of a time-varying spectral density operator of which the properties are studied and uniqueness is derived. Finally, we provide a consistent nonparametric estimator of this operator and show it is asymptotically Gaussian using a weaker tightness criterion than what is usually deemed necessary.

stat.ME↗
arXiv2016

Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions

Hawkes (1971) introduced a powerful multivariate point process model of mutually exciting processes to explain causal structure in data. In this paper it is shown that the Granger causality structure of such processes is fully encoded in the corresponding link functions of the model. A new nonparametric estimator of the link functions based on a time-discretized version of the point process is introduced by using an infinite order autoregression. Consistency of the new estimator is derived. The estimator is applied to simulated data and to neural spike train data from the spinal dorsal horn of a rat.

math.ST↗
arXiv2012

Fitting Graphical Interaction Models to Multivariate Time Series

Graphical interaction models have become an important tool for analysing multivariate time series. In these models, the interrelationships among the components of a time series are described by undirected graphs in which the vertices depict the components while the edges indictate possible dependencies between the components. Current methods for the identification of the graphical structure are based on nonparametric spectral stimation, which prevents application of common model selection strategies. In this paper, we present a parametric approach for graphical interaction modelling of multivariate stationary time series. The proposed models generalize covariance selection models to the time series setting and are formulated in terms of inverse covariances. We show that these models correspond to vector autoregressive models under conditional independence constraints encoded by undirected graphs. Furthermore, we discuss maximum likelihood estimation based on Whittle's approximation to the log-likelihood function and propose an iterative method for solving the resulting likelihood equations. The concepts are illustrated by an example.

stat.ME↗
arXiv2012

Causal Reasoning in Graphical Time Series Models

We propose a definition of causality for time series in terms of the effect of an intervention in one component of a multivariate time series on another component at some later point in time. Conditions for identifiability, comparable to the back-door and front-door criteria, are presented and can also be verified graphically. Computation of the causal effect is derived and illustrated for the linear case.

stat.ME↗
arXiv2011

A note on global Markov properties for mixed graphs

Global Markov properties in mixed graphs are usually formulated in terms of the path-oriented m-separation or by use of augmented graphs (similar to moral graphs in the case of directed acyclic graphs). We provide an alternative characterization that can be easily implemented.

stat.ME↗
arXiv2011

Graphical modelling of multivariate time series

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with non-linear dependencies. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs each component series is represented by a single vertex and directed edges indicate possible Granger-causal relationships between variables while undirected edges are used to map the contemporaneous dependence structure. We introduce various notions of Granger-causal Markov properties and discuss the relationships among them and to other Markov properties that can be applied in this context.

math.ST↗
arXiv2008

Computing maximum likelihood estimates in recursive linear models with correlated errors

In recursive linear models, the multivariate normal joint distribution of all variables exhibits a dependence structure induced by a recursive (or acyclic) system of linear structural equations. These linear models have a long tradition and appear in seemingly unrelated regressions, structural equation modelling, and approaches to causal inference. They are also related to Gaussian graphical models via a classical representation known as a path diagram. Despite the models' long history, a number of problems remain open. In this paper, we address the problem of computing maximum likelihood estimates in the subclass of `bow-free' recursive linear models. The term `bow-free' refers to the condition that the errors for variables $i$ and $j$ be uncorrelated if variable $i$ occurs in the structural equation for variable $j$. We introduce a new algorithm, termed Residual Iterative Conditional Fitting (RICF), that can be implemented using only least squares computations. In contrast to existing algorithms, RICF has clear convergence properties and finds parameter estimates in closed form whenever possible.

math.ST↗
arXiv2005

Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property

The AMP Markov property is a recently proposed alternative Markov property for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced LWF Markov property that is coherent with data-generation by natural block-recursive regressions. In this paper, we show that maximum likelihood estimates in Gaussian AMP chain graph models can be obtained by combining generalized least squares and iterative proportional fitting to an iterative algorithm. In an appendix, we give useful convergence results for iterative partial maximization algorithms that apply in particular to the described algorithm.

math.ST↗