Tracking the risk of a deployed model and detecting harmful distribution shifts

When deployed in the real world, machine learning models inevitably encounter changes in the data distribution, and certain -- but not all -- distribution shifts could result in significant performance degradation. In practice, it may make sense to ignore benign shifts, under which the performance of a deployed model does not degrade substantially, making interventions by a human expert (or model retraining) unnecessary. While several works have developed tests for distribution shifts, these typically either use non-sequential methods, or detect arbitrary shifts (benign or harmful), or both. We argue that a sensible method for firing off a warning has to both (a) detect harmful shifts while ignoring benign ones, and (b) allow continuous monitoring of model performance without increasing the false alarm rate. In this work, we design simple sequential tools for testing if the difference between source (training) and target (test) distributions leads to a significant increase in a risk function of interest, like accuracy or calibration. Recent advances in constructing time-uniform confidence sequences allow efficient aggregation of statistical evidence accumulated during the tracking process. The designed framework is applicable in settings where (some) true labels are revealed after the prediction is performed, or when batches of labels become available in a delayed fashion. We demonstrate the efficacy of the proposed framework through an extensive empirical study on a collection of simulated and real datasets.Comment: Accepted as a conference paper at ICLR 202

The Emergence of Gravitational Wave Science: 100 Years of Development of Mathematical Theory, Detectors, Numerical Algorithms, and Data Analysis Tools

On September 14, 2015, the newly upgraded Laser Interferometer Gravitational-wave Observatory (LIGO) recorded a loud gravitational-wave (GW) signal, emitted a billion light-years away by a coalescing binary of two stellar-mass black holes. The detection was announced in February 2016, in time for the hundredth anniversary of Einstein's prediction of GWs within the theory of general relativity (GR). The signal represents the first direct detection of GWs, the first observation of a black-hole binary, and the first test of GR in its strong-field, high-velocity, nonlinear regime. In the remainder of its first observing run, LIGO observed two more signals from black-hole binaries, one moderately loud, another at the boundary of statistical significance. The detections mark the end of a decades-long quest, and the beginning of GW astronomy: finally, we are able to probe the unseen, electromagnetically dark Universe by listening to it. In this article, we present a short historical overview of GW science: this young discipline combines GR, arguably the crowning achievement of classical physics, with record-setting, ultra-low-noise laser interferometry, and with some of the most powerful developments in the theory of differential geometry, partial differential equations, high-performance computation, numerical analysis, signal processing, statistical inference, and data science. Our emphasis is on the synergy between these disciplines, and how mathematics, broadly understood, has historically played, and continues to play, a crucial role in the development of GW science. We focus on black holes, which are very pure mathematical solutions of Einstein's gravitational-field equations that are nevertheless realized in Nature, and that provided the first observed signals.Comment: 41 pages, 5 figures. To appear in Bulletin of the American Mathematical Societ

The Conformal Bootstrap: Theory, Numerical Techniques, and Applications

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same time sit at the heart of our modern understanding of quantum field theory. For decades it has been a dream to study these intricate strongly coupled theories nonperturbatively using symmetries and other consistency conditions. This idea, called the conformal bootstrap, saw some successes in two dimensions but it is only in the last ten years that it has been fully realized in three, four, and other dimensions of interest. This renaissance has been possible both due to significant analytical progress in understanding how to set up the bootstrap equations and the development of numerical techniques for finding or constraining their solutions. These developments have led to a number of groundbreaking results, including world record determinations of critical exponents and correlation function coefficients in the Ising and $O(N)$ models in three dimensions. This article will review these exciting developments for newcomers to the bootstrap, giving an introduction to conformal field theories and the theory of conformal blocks, describing numerical techniques for the bootstrap based on convex optimization, and summarizing in detail their applications to fixed points in three and four dimensions with no or minimal supersymmetry.Comment: 81 pages, double column, 58 figures; v3: updated references, minor typos correcte

How can humans leverage machine learning? From Medical Data Wrangling to Learning to Defer to Multiple Experts

Mención Internacional en el título de doctorThe irruption of the smartphone into everyone’s life and the ease with which we digitise or record any data supposed an explosion of quantities of data. Smartphones, equipped with advanced cameras and sensors, have empowered individuals to capture moments and contribute to the growing pool of data. This data-rich landscape holds great promise for research, decision-making, and personalized applications. By carefully analyzing and interpreting this wealth of information, valuable insights, patterns, and trends can be uncovered. However, big data is worthless in a vacuum. Its potential value is unlocked only when leveraged to drive decision-making. In recent times we have been participants of the outburst of artificial intelligence: the development of computer systems and algorithms capable of perceiving, reasoning, learning, and problem-solving, emulating certain aspects of human cognitive abilities. Nevertheless, our focus tends to be limited, merely skimming the surface of the problem, while the reality is that the application of machine learning models to data introduces is usually fraught. More specifically, there are two crucial pitfalls frequently neglected in the field of machine learning: the quality of the data and the erroneous assumption that machine learning models operate autonomously. These two issues have established the foundation for the motivation driving this thesis, which strives to offer solutions to two major associated challenges: 1) dealing with irregular observations and 2) learning when and who should we trust. The first challenge originates from our observation that the majority of machine learning research primarily concentrates on handling regular observations, neglecting a crucial technological obstacle encountered in practical big-data scenarios: the aggregation and curation of heterogeneous streams of information. Before applying machine learning algorithms, it is crucial to establish robust techniques for handling big data, as this specific aspect presents a notable bottleneck in the creation of robust algorithms. Data wrangling, which encompasses the extraction, integration, and cleaning processes necessary for data analysis, plays a crucial role in this regard. Therefore, the first objective of this thesis is to tackle the frequently disregarded challenge of addressing irregularities within the context of medical data. We will focus on three specific aspects. Firstly, we will tackle the issue of missing data by developing a framework that facilitates the imputation of missing data points using relevant information derived from alternative data sources or past observations. Secondly, we will move beyond the assumption of homogeneous observations, where only one statistical data type (such as Gaussian) is considered, and instead, work with heterogeneous observations. This means that different data sources can be represented by various statistical likelihoods, such as Gaussian, Bernoulli, categorical, etc. Lastly, considering the temporal enrichment of todays collected data and our focus on medical data, we will develop a novel algorithm capable of capturing and propagating correlations among different data streams over time. All these three problems are addressed in our first contribution which involves the development of a novel method based on Deep Generative Models (DGM) using Variational Autoencoders (VAE). The proposed model, the Sequential Heterogeneous Incomplete VAE (Shi- VAE), enables the aggregation of multiple heterogeneous data streams in a modular manner, taking into consideration the presence of potential missing data. To demonstrate the feasibility of our approach, we present proof-of-concept results obtained from a real database generated through continuous passive monitoring of psychiatric patients. Our second challenge relates to the misbelief that machine learning algorithms can perform independently. However, this notion that AI systems can solely account for automated decisionmaking, especially in critical domains such as healthcare, is far from reality. Our focus now shifts towards a specific scenario where the algorithm has the ability to make predictions independently or alternatively defer the responsibility to a human expert. The purpose of including the human is not to obtain jsut better performance, but also more reliable and trustworthy predictions we can rely on. In reality, however, important decisions are not made by one person but are usually committed by an ensemble of human experts. With this in mind, two important questions arise: 1) When should the human or the machine bear responsibility and 2) among the experts, who should we trust? To answer the first question, we will employ a recent theory known as Learning to defer (L2D). In L2D we are not only interested in abstaining from prediction but also in understanding the humans confidence for making such prediction. thus deferring only when the human is more likely to be correct. The second question about who to defer among a pool of experts has not been yet answered in the L2D literature, and this is what our contributions aim to provide. First, we extend the two yet proposed consistent surrogate losses in the L2D literature to the multiple-expert setting. Second, we study the frameworks ability to estimate the probability that a given expert correctly predicts and assess whether the two surrogate losses are confidence calibrated. Finally, we propose a conformal inference technique that chooses a subset of experts to query when the system defers. Ensembling experts based on confidence levels is vital to optimize human-machine collaboration. In conclusion, this doctoral thesis has investigated two cases where humans can leverage the power of machine learning: first, as a tool to assist in data wrangling and data understanding problems and second, as a collaborative tool where decision-making can be automated by the machine or delegated to human experts, fostering more transparent and trustworthy solutions.La irrupción de los smartphones en la vida de todos y la facilidad con la que digitalizamos o registramos cualquier situación ha supuesto una explosión en la cantidad de datos. Los teléfonos, equipados con cámaras y sensores avanzados, han contribuido a que las personas puedann capturar más momentos, favoreciendo así el creciente conjunto de datos. Este panorama repleto de datos aporta un gran potencial de cara a la investigación, la toma de decisiones y las aplicaciones personalizadas. Mediante el análisis minucioso y una cuidada interpretación de esta abundante información, podemos descubrir valiosos patrones, tendencias y conclusiones Sin embargo, este gran volumen de datos no tiene valor por si solo. Su potencial se desbloquea solo cuando se aprovecha para impulsar la toma de decisiones. En tiempos recientes, hemos sido testigos del auge de la inteligencia artificial: el desarrollo de sistemas informáticos y algoritmos capaces de percibir, razonar, aprender y resolver problemas, emulando ciertos aspectos de las capacidades cognitivas humanas. No obstante, solemos centrarnos solo en la superficie del problema mientras que la realidad es que la aplicación de modelos de aprendizaje automático a los datos presenta desafíos significativos. Concretamente, se suelen pasar por alto dos problemas cruciales en el campo del aprendizaje automático: la calidad de los datos y la suposición errónea de que los modelos de aprendizaje automático pueden funcionar de manera autónoma. Estos dos problemas han sido el fundamento de la motivación que impulsa esta tesis, que se esfuerza en ofrecer soluciones a dos desafíos importantes asociados: 1) lidiar con datos irregulares y 2) aprender cuándo y en quién debemos confiar. El primer desafío surge de nuestra observación de que la mayoría de las investigaciones en aprendizaje automático se centran principalmente en manejar datos regulares, descuidando un obstáculo tecnológico crucial que se encuentra en escenarios prácticos con gran cantidad de datos: la agregación y el curado de secuencias heterogéneas. Antes de aplicar algoritmos de aprendizaje automático, es crucial establecer técnicas robustas para manejar estos datos, ya que est problemática representa un cuello de botella claro en la creación de algoritmos robustos. El procesamiento de datos (en concreto, nos centraremos en el término inglés data wrangling), que abarca los procesos de extracción, integración y limpieza necesarios para el análisis de datos, desempeña un papel crucial en este sentido. Por lo tanto, el primer objetivo de esta tesis es abordar el desafío normalmente paso por alto de tratar datos irregulare. Específicamente, bajo el contexto de datos médicos. Nos centraremos en tres aspectos principales. En primer lugar, abordaremos el problema de los datos perdidos mediante el desarrollo de un marco que facilite la imputación de estos datos perdidos utilizando información relevante obtenida de fuentes de datos de diferente naturalaeza u observaciones pasadas. En segundo lugar, iremos más allá de la suposición de lidiar con observaciones homogéneas, donde solo se considera un tipo de dato estadístico (como Gaussianos) y, en su lugar, trabajaremos con observaciones heterogéneas. Esto significa que diferentes fuentes de datos pueden estar representadas por diversas distribuciones de probabilidad, como Gaussianas, Bernoulli, categóricas, etc. Por último, teniendo en cuenta el enriquecimiento temporal de los datos hoy en día y nuestro enfoque directo sobre los datos médicos, propondremos un algoritmo innovador capaz de capturar y propagar la correlación entre diferentes flujos de datos a lo largo del tiempo. Todos estos tres problemas se abordan en nuestra primera contribución, que implica el desarrollo de un método basado en Modelos Generativos Profundos (Deep Genarative Model en inglés) utilizando Autoencoders Variacionales (Variational Autoencoders en ingés). El modelo propuesto, Sequential Heterogeneous Incomplete VAE (Shi-VAE), permite la agregación de múltiples flujos de datos heterogéneos de manera modular, teniendo en cuenta la posible presencia de datos perdidos. Para demostrar la viabilidad de nuestro enfoque, presentamos resultados de prueba de concepto obtenidos de una base de datos real generada a través del monitoreo continuo pasivo de pacientes psiquiátricos. Nuestro segundo desafío está relacionado con la creencia errónea de que los algoritmos de aprendizaje automático pueden funcionar de manera independiente. Sin embargo, esta idea de que los sistemas de inteligencia artificial pueden ser los únicos responsables en la toma de decisione, especialmente en dominios críticos como la atención médica, está lejos de la realidad. Ahora, nuestro enfoque se centra en un escenario específico donde el algoritmo tiene la capacidad de realizar predicciones de manera independiente o, alternativamente, delegar la responsabilidad en un experto humano. La inclusión del ser humano no solo tiene como objetivo obtener un mejor rendimiento, sino también obtener predicciones más transparentes y seguras en las que podamos confiar. En la realidad, sin embargo, las decisiones importantes no las toma una sola persona, sino que generalmente son el resultado de la colaboración de un conjunto de expertos. Con esto en mente, surgen dos preguntas importantes: 1) ¿Cuándo debe asumir la responsabilidad el ser humano o cuándo la máquina? y 2) de entre los expertos, ¿en quién debemos confiar? Para responder a la primera pregunta, emplearemos una nueva teoría llamada Learning to defer (L2D). En L2D, no solo estamos interesados en abstenernos de hacer predicciones, sino también en comprender cómo de seguro estará el experto para hacer dichas predicciones, diferiendo solo cuando el humano sea más probable en predecir correcatmente. La segunda pregunta sobre a quién deferir entre un conjunto de expertos aún no ha sido respondida en la literatura de L2D, y esto es precisamente lo que nuestras contribuciones pretenden proporcionar. En primer lugar, extendemos las dos primeras surrogate losses consistentes propuestas hasta ahora en la literatura de L2D al contexto de múltiples expertos. En segundo lugar, estudiamos la capacidad de estos modelos para estimar la probabilidad de que un experto dado haga predicciones correctas y evaluamos si estas surrogate losses están calibradas en términos de confianza. Finalmente, proponemos una técnica de conformal inference que elige un subconjunto de expertos para consultar cuando el sistema decide diferir. Esta combinación de expertos basada en los respectivos niveles de confianza es fundamental para optimizar la colaboración entre humanos y máquinas En conclusión, esta tesis doctoral ha investigado dos casos en los que los humanos pueden aprovechar el poder del aprendizaje automático: primero, como herramienta para ayudar en problemas de procesamiento y comprensión de datos y, segundo, como herramienta colaborativa en la que la toma de decisiones puede ser automatizada para ser realizada por la máquina o delegada a expertos humanos, fomentando soluciones más transparentes y seguras.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Joaquín Míguez Arenas.- Secretario: Juan José Murillo Fuentes.- Vocal: Mélanie Natividad Fernández Pradie

UNDERSTANDING CONDITIONAL MODES OF ACTIONS IN CHEMICAL-INDUCED TOXICITY USING RULE MODELS

It is estimated that 115 million animals are used in experimental testing each year. Hence, shifting efforts toward alternative methods for toxicity assessment is essential. However, slow regulatory acceptance of new approaches is governed by knowledge gaps in toxicity modes of action. In this thesis, I describe these challenges and the use of in vitro screening as an alternative of animal testing. I also discuss common data-based methods to derive hypotheses about toxicity modes of actions, and the associated limitations in capturing multiple biological perturbations. I applied novel data-based workflows, using rule models, to prioritize in vitro assays predictive of toxicity as well as to detect significant polypharmacology profiles. I explain how constraints were applied to rule-based models to inform meaningful mechanistic interpretation for two toxicity endpoints: rat hepatotoxicity and acute toxicity. I compared assays selected, by rules, for predicting hepatotoxicity with endpoints used in in vitro models from commercial sources. An overlap was observed including cytochrome activity, mitochondrial toxicity and immunological responses. However, nuclear receptor activity, identified in rules, is not currently covered in commercial setups. I also demonstrate that endocrine disruption endpoints extrapolate better into in vivo toxicity when a set of specific conditions are met, such as physicochemical properties associated with good bioavailability. Next, I examined synergistic interactions between conditions in rules describing acute toxicity. I gained novel insights into how specific stressors potentiate the perturbation by known key events, such as acetylcholinesterase inhibition and neuro-signalling disruption. I show that examining polypharmacology profiles is particularly important at low bioactive potencies. Further, the overall predictive performance of rules describing acute toxicity was tested against a benchmark Random Forest model in a conformal prediction framework. Irrespective to the data type used in the training, the models were prone to bias over compounds promiscuity, by which high promiscuous compounds were more likely to be predicted as toxic. Overall, the studies conducted in this thesis provide novel insights into molecular mechanisms of toxicity, namely hepatotoxicity and acute toxicity, and with regards to chemical properties and polypharmacology. This knowledge can be used to improve the utility and design of alternative methods for toxicity, and hence, accelerate the regulatory acceptance.Islamic Development Bank Cambridge Trust Fun

Distributionally Robust Statistical Verification with Imprecise Neural Networks

A particularly challenging problem in AI safety is providing guarantees on the behavior of high-dimensional autonomous systems. Verification approaches centered around reachability analysis fail to scale, and purely statistical approaches are constrained by the distributional assumptions about the sampling process. Instead, we pose a distributionally robust version of the statistical verification problem for black-box systems, where our performance guarantees hold over a large family of distributions. This paper proposes a novel approach based on a combination of active learning, uncertainty quantification, and neural network verification. A central piece of our approach is an ensemble technique called Imprecise Neural Networks, which provides the uncertainty to guide active learning. The active learning uses an exhaustive neural-network verification tool Sherlock to collect samples. An evaluation on multiple physical simulators in the openAI gym Mujoco environments with reinforcement-learned controllers demonstrates that our approach can provide useful and scalable guarantees for high-dimensional systems

Lectures on D-branes, gauge theories and Calabi-Yau singularities

These lectures, given at the Chinese Academy of Sciences for the BeiJing/HangZhou International Summer School in Mathematical Physics, are intended to introduce, to the beginning student in string theory and mathematical physics, aspects of the rich and beautiful subject of D-brane gauge theories constructed from local Calabi-Yau spaces. Topics such as orbifolds, toric singularities, del Pezzo surfaces as well as chaotic duality will be covered