A Survey of Tuning Parameter Selection for High-dimensional Regression

Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of penalized regression relies crucially on the choice of the tuning parameter, which determines the amount of regularization and hence the sparsity level of the fitted model. The optimal choice of tuning parameter depends on both the structure of the design matrix and the unknown random error distribution (variance, tail behavior, etc). This article reviews the current literature of tuning parameter selection for high-dimensional regression from both theoretical and practical perspectives. We discuss various strategies that choose the tuning parameter to achieve prediction accuracy or support recovery. We also review several recently proposed methods for tuning-free high-dimensional regression.Comment: 28 pages, 2 figure

Resampling-based Confidence Intervals for Model-free Robust Inference on Optimal Treatment Regimes

We propose a new procedure for inference on optimal treatment regimes in the model-free setting, which does not require to specify an outcome regression model. Existing model-free estimators for optimal treatment regimes are usually not suitable for the purpose of inference, because they either have nonstandard asymptotic distributions or do not necessarily guarantee consistent estimation of the parameter indexing the Bayes rule due to the use of surrogate loss. We first study a smoothed robust estimator that directly targets the parameter corresponding to the Bayes decision rule for optimal treatment regimes estimation. This estimator is shown to have an asymptotic normal distribution. Furthermore, we verify that a resampling procedure provides asymptotically accurate inference for both the parameter indexing the optimal treatment regime and the optimal value function. A new algorithm is developed to calculate the proposed estimator with substantially improved speed and stability. Numerical results demonstrate the satisfactory performance of the new methods.Comment: 59 pages, 8 table

Differential-Equation Constrained Optimization With Stochasticity

Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured data. The formulation is powerful and widely used in many sciences and engineering fields. However, one crucial assumption is that the unknown parameter must be deterministic. In reality, however, many problems are stochastic in nature, and the unknown parameter is random. The challenge then becomes recovering the full distribution of this unknown random parameter. It is a much more complex task. In this paper, we examine this problem in a general setting. In particular, we conceptualize the PDE solver as a push-forward map that pushes the parameter distribution to the generated data distribution. This way, the SDE-constrained optimization translates to minimizing the distance between the generated distribution and the measurement distribution. We then formulate a gradient-flow equation to seek the ground-truth parameter probability distribution. This opens up a new paradigm for extending many techniques in PDE-constrained optimization to that for systems with stochasticity.Comment: 27 pages, 7 figure

Analytical method developments of antibody drug conjugates and disease biomarkers in microdialysis samples

This dissertation focuses on developing analytical methods to study biomarkers in different pharmaceutical samples. Three different analytical methods were developed for microdialysis samples and antibody drug conjugates as anti-tumor drug. The first part of this dissertation is to develop a capillary electrophoresis with laser induced fluorescence (CE-LIF) method to monitor the change of amino acids in rat brain microdialysate as biomarkers of oxidative stress in epileptic seizures. Ornithine and citrulline was successfully separated and quantified. 3-Mercaptopropionic acid (3-MPA) was administrated to rat brain hippocampus region as a convulsant to induce epileptic seizures to free-moving rats. An increase of citrulline and ornithine level was observed after the seizure, and this confirmed nitric oxide were produced in epileptic seizures. In the second project, a high-performance liquid chromatography with mass spectrometry (HPLC-MS) method is developed to simultaneously monitor the change of 13 eicosanoids as biomarkers in rat colon microdialysate to study the enzymatic pathways of inflammatory bowel disease. Moreover, cyclodextrin were added into microdialysis perfusate to improve the microdialysis recovery and solubility of the hydrophobic eicosanoids. The last part is to utilize enzyme deconjugation and HPLC-UV-Vis to study the stability and compatibility of antibody drug conjugates (ADCs). Bromelain was utilized as an enzyme to fully cleave off the small molecule cytotoxic drug from the ADCs. This allows a direct analysis of the small molecule cytotoxic drug on the ADCs. The stability of antibody drug conjugates was studied with LC-UV-Vis after mixing with other conjugation reagents and formulation excipients

Análisis de la comunicación de las universidades españolas en Twitter en el marco de la tercera misión

Mención Interancional en el título de doctorEl objetivo de esta investigación es analizar el uso que las universidades españolas están haciendo de Twitter en el marco de la tercera misión de la universidad. Este concepto surge en los años 80 del siglo pasado y se ve hoy fortalecido ante la reciente irrupción de las muchas y muy variadas posibilidades que ofrecen las tecnologías digitales. Para examinar este uso, hemos llevado a cabo un análisis del contenido de la actividad generada en Twitter por las universidades españolas más influyentes en este servicio. Este análisis ha sido doble: por un lado, hemos estudiado la morfología de las cuentas a partir de la información que ofrece Twitonomy y por otro hemos llevado a cabo un análisis del contenido de los mensajes publicados entre marzo y junio de 2016 por las 30 universidades españolas con mayores índices Klout1. En este periodo, las 30 universidades analizadas publicaron un total de 35.167 tuits, que categorizamos a partir de un código que incluye variables formales y otras relativas al contenido de los mensajes. Los resultados demuestran que las universidades analizadas han normalizado el empleo de Twitter, servicio que utilizan como un canal de comunicación adicional. La Universidad de Sevilla fue la más activa, ya que publicó una media de 37,21 mensajes por día. En general, las universidades estudiadas destinaron un 68,8% de su producción a divulgar información promocional de la propia universidad, algo un poco alejado de lo que en principio cabría esperar de una universidad que se esfuerza por fortalecer su tercera misión. Además, las universidades analizadas infrautilizaron las posibilidades que ofrece este servicio para enriquecer sus contribuciones a través de material multimedia en forma de fotos, audios, vídeos, emoticonos o GIFs. En este punto, sólo destaca el empleo de fotos en el 52,1% del total de la muestra. Los resultados también reflejan que, con alguna excepción, la mayor parte de las universidades españolas desaprovecharon de forma evidente el potencial que ofrece Twitter para crear comunidad. Confiamos en que la relación sistematizada de buenas prácticas que incluimos en el segundo capítulo contribuya a mejorar la comunicación de las universidades en Twitter de modo que éstas puedan aprovechar más el potencial multimedia que ofrece el servicio y se animen a recurrir a él para fortalecer su tercera misión.The aim of this doctoral dissertation is to analyze how Spanish universities are using Twitter within the framework of the third mission of the university. This concept emerged in the 80s and is today strengthened by the recent irruption of the many and varied possibilities offered by the digital technologies. To examine this use, we have carried out a content analysis of the activity on Twitter of some of the most influential Spanish universities. This analysis has two parts: on one hand, we have examined the morphology of the accounts based on the information offered by Twitonomy; on the other hand, we have carried out a content analysis of the updates posted on Twitter by the 30 Spanish universities with higher Klout indexes between March and June 2016. In this period, the 30 universities analyzed, published a total of 35,167 tweets, which we categorized according to a code that included some formal variables and other ones related to the content of the messages. The results show that the examined universities have normalized the use of Twitter, used as an additional channel for communication. The University of Seville was the most active, since it posted an average of 37.21 messages per day. In general, the universities allocated 68.8% of their production to issue promotional information of its own university, something a bit far off from what would normally be expected from a university that strives to strengthen its third mission. In addition, the analyzed universities underestimated the possibilities that this service offers in order to enrich their contributions through multimedia material such as photos, audios, videos, emojis or GIFs. At this point, only the use of pictures stands out in 52% of the total sample. The results also show that, with some exceptions, the largest part of the Spanish universities did not take full advantage of the great potential that Twitter provides for community engagement. We hope that the systematized collection of good practices included in the second chapter can contribute to improve the communication of universities on Twitter so that they can take more advantage of the multimedia potential offered by the service and use it to strengthen their third mission.Programa Oficial de Doctorado en Investigación en Medios de ComunicaciónPresidente: José Antonio Ruiz San Román.- Secretario: Juan Pedro Molina Cañabate.- Vocal: Rogério Christofolett

Suppressing Instability in a Vlasov-Poisson System by an External Electric Field Through Constrained Optimization

Fusion energy offers the potential for the generation of clean, safe, and nearly inexhaustible energy. While notable progress has been made in recent years, significant challenges persist in achieving net energy gain. Improving plasma confinement and stability stands as a crucial task in this regard and requires optimization and control of the plasma system. In this work, we deploy a PDE-constrained optimization formulation that uses a kinetic description for plasma dynamics as the constraint. This is to optimize, over all possible controllable external electric fields, the stability of the plasma dynamics under the condition that the Vlasov--Poisson (VP) equation is satisfied. For computing the functional derivative with respect to the external field in the optimization updates, the adjoint equation is derived. Furthermore, in the discrete setting, where we employ the semi-Lagrangian method as the forward solver, we also explicitly formulate the corresponding adjoint solver and the gradient as the discrete analogy to the adjoint equation and the Frechet derivative. A distinct feature we observed of this constrained optimization is the complex landscape of the objective function and the existence of numerous local minima, largely due to the hyperbolic nature of the VP system. To overcome this issue, we utilize a gradient-accelerated genetic algorithm, leveraging the advantages of the genetic algorithm's exploration feature to cover a broader search of the solution space and the fast local convergence aided by the gradient information. We show that our algorithm obtains good electric fields that are able to maintain a prescribed profile in a beam shaping problem and uses nonlinear effects to suppress plasma instability in a two-stream configuration