15,587 research outputs found
Model Diagnostics meets Forecast Evaluation: Goodness-of-Fit, Calibration, and Related Topics
Principled forecast evaluation and model diagnostics are vital in fitting probabilistic models and forecasting outcomes of interest. A common principle is that fitted or predicted distributions ought to be calibrated, ideally in the sense that the outcome is indistinguishable from a random draw from the posited distribution. Much of this thesis is centered on calibration properties of various types of forecasts.
In the first part of the thesis, a simple algorithm for exact multinomial goodness-of-fit tests is proposed. The algorithm computes exact -values based on various test statistics, such as the log-likelihood ratio and Pearson\u27s chi-square. A thorough analysis shows improvement on extant methods. However, the runtime of the algorithm grows exponentially in the number of categories and hence its use is limited.
In the second part, a framework rooted in probability theory is developed, which gives rise to hierarchies of calibration, and applies to both predictive distributions and stand-alone point forecasts. Based on a general notion of conditional T-calibration, the thesis introduces population versions of T-reliability diagrams and revisits a score decomposition into measures of miscalibration, discrimination, and uncertainty. Stable and efficient estimators of T-reliability diagrams and score components arise via nonparametric isotonic regression and the pool-adjacent-violators algorithm. For in-sample model diagnostics, a universal coefficient of determination is introduced that nests and reinterprets the classical in least squares regression.
In the third part, probabilistic top lists are proposed as a novel type of prediction in classification, which bridges the gap between single-class predictions and predictive distributions. The probabilistic top list functional is elicited by strictly consistent evaluation metrics, based on symmetric proper scoring rules, which admit comparison of various types of predictions
A scalable solution for the extended multi-channel facility location problem
We study the extended version of the non-uniform, capacitated facility
location problem with multiple fulfilment channels between the facilities and
clients, each with their own channel capacities and service cost. Though the
problem has been extensively studied in the literature, all the prior works
assume a single channel of fulfilment, and the existing methods based on linear
programming, primal-dual relationships, local search heuristics etc. do not
scale for a large supply chain system involving millions of decision variables.
Using the concepts of sub-modularity and optimal transport theory, we present a
scalable algorithm for determining the set of facilities to be opened under a
cardinality constraint. By introducing various schemes such as: (i) iterative
facility selection using incremental gain, (ii) approximation of the linear
program using novel multi-stage Sinkhorn iterations, (iii) creation of
facilities one for each fulfilment channel etc., we develop a fast but a tight
approximate solution, requiring
instances of optimal transport problems to select k facilities from m options,
each solvable in linear time. Our algorithm is implicitly endowed with all the
theoretical guarantees enjoyed by submodular maximisation problems and the
Sinkhorn distances. When compared against the state-of-the-art commercial MILP
solvers, we obtain a 100-fold speedup in computation, while the difference in
objective values lies within a narrow range of 3%
Exploring the Structure of Scattering Amplitudes in Quantum Field Theory: Scattering Equations, On-Shell Diagrams and Ambitwistor String Models in Gauge Theory and Gravity
In this thesis I analyse the structure of scattering amplitudes in super-symmetric gauge and gravitational theories in four dimensional spacetime, starting with a detailed review of background material accessible to a non-expert. I then analyse the 4D scattering equations, developing the theory of how they can be used to express scattering amplitudes at tree level. I go on to explain how the equations can be solved numerically using a Monte Carlo algorithm, and introduce my Mathematica package treeamps4dJAF which performs these calculations. Next I analyse the relation between the 4D scattering equations and on-shell diagrams in N = 4 super Yang-Mills, which provides a new perspective on the tree level amplitudes of the theory. I apply a similar analysis to N = 8 supergravity, developing the theory of on-shell diagrams to derive new Grassmannian integral formulae for the amplitudes of the theory. In both theories I derive a new worldsheet expression for the 4 point one loop amplitude supported on 4D scattering equations. Finally I use 4D ambitwistor string theory to analyse scattering amplitudes in N = 4 conformal supergravity, deriving new worldsheet formulae for both plane wave and non-plane wave amplitudes supported on 4D scattering equations. I introduce a new prescription to calculate the derivatives of on-shell variables with respect to momenta, and I use this to show that certain non-plane wave amplitudes can be calculated as momentum derivatives of amplitudes with plane wave states
Annals [...].
Pedometrics: innovation in tropics; Legacy data: how turn it useful?; Advances in soil sensing; Pedometric guidelines to systematic soil surveys.Evento online. Coordenado por: Waldir de Carvalho Junior, Helena Saraiva Koenow Pinheiro, Ricardo Simão Diniz Dalmolin
A suite of quantum algorithms for the shortestvector problem
Crytography has come to be an essential part of the cybersecurity infrastructure that provides a safe environment for communications in an increasingly connected world. The advent of quantum computing poses a threat to the foundations of the current widely-used cryptographic model, due to the breaking of most of the cryptographic algorithms used to provide confidentiality, authenticity, and more. Consequently a new set of cryptographic protocols have been designed to be secure against quantum computers, and are collectively known as post-quantum cryptography (PQC). A forerunner among PQC is lattice-based cryptography, whose security relies upon the hardness of a number of closely related mathematical problems, one of which is known as the shortest vector problem (SVP).
In this thesis I describe a suite of quantum algorithms that utilize the energy minimization principle to attack the shortest vector problem. The algorithms outlined span the gate-model and continuous time quantum computing, and explore methods of parameter optimization via variational methods, which are thought to be effective on near-term quantum computers. The performance of the algorithms are analyzed numerically, analytically, and on quantum hardware where possible. I explain how the results obtained in the pursuit of solving SVP apply more broadly to quantum algorithms seeking to solve general real-world problems; minimize the effect of noise on imperfect hardware; and improve efficiency of parameter optimization.Open Acces
Development of in-vitro in-silico technologies for modelling and analysis of haematological malignancies
Worldwide, haematological malignancies are responsible for roughly 6% of all the cancer-related deaths. Leukaemias are one of the most severe types of cancer, as only about 40% of the patients have an overall survival of 10 years or more. Myelodysplastic Syndrome (MDS), a pre-leukaemic condition, is a blood disorder characterized by the presence of dysplastic, irregular, immature cells, or blasts, in the peripheral blood (PB) and in the bone marrow (BM), as well as multi-lineage cytopenias.
We have created a detailed, lineage-specific, high-fidelity in-silico erythroid model that incorporates known biological stimuli (cytokines and hormones) and a competing diseased haematopoietic population, correctly capturing crucial biological checkpoints (EPO-dependent CFU-E differentiation) and replicating the in-vivo erythroid differentiation dynamics. In parallel, we have also proposed a long-term, cytokine-free 3D cell culture system for primary MDS cells, which was firstly optimized using easily-accessible healthy controls. This system enabled long-term (24-day) maintenance in culture with high (>75%) cell viability, promoting spontaneous expansion of erythroid phenotypes (CD71+/CD235a+) without the addition of any exogenous cytokines. Lastly, we have proposed a novel in-vitro in-silico framework using GC-MS metabolomics for the metabolic profiling of BM and PB plasma, aiming not only to discretize between haematological conditions but also to sub-classify MDS patients, potentially based on candidate biomarkers. Unsupervised multivariate statistical analysis showed clear intra- and inter-disease separation of samples of 5 distinct haematological malignancies, demonstrating the potential of this approach for disease characterization.
The work herein presented paves the way for the development of in-vitro in-silico technologies to better, characterize, diagnose, model and target haematological malignancies such as MDS and AML.Open Acces
Foundations for programming and implementing effect handlers
First-class control operators provide programmers with an expressive and efficient
means for manipulating control through reification of the current control state as a first-class object, enabling programmers to implement their own computational effects and
control idioms as shareable libraries. Effect handlers provide a particularly structured
approach to programming with first-class control by naming control reifying operations
and separating from their handling.
This thesis is composed of three strands of work in which I develop operational
foundations for programming and implementing effect handlers as well as exploring
the expressive power of effect handlers.
The first strand develops a fine-grain call-by-value core calculus of a statically
typed programming language with a structural notion of effect types, as opposed to the
nominal notion of effect types that dominates the literature. With the structural approach,
effects need not be declared before use. The usual safety properties of statically typed
programming are retained by making crucial use of row polymorphism to build and
track effect signatures. The calculus features three forms of handlers: deep, shallow,
and parameterised. They each offer a different approach to manipulate the control state
of programs. Traditional deep handlers are defined by folds over computation trees,
and are the original con-struct proposed by Plotkin and Pretnar. Shallow handlers are
defined by case splits (rather than folds) over computation trees. Parameterised handlers
are deep handlers extended with a state value that is threaded through the folds over
computation trees. To demonstrate the usefulness of effects and handlers as a practical
programming abstraction I implement the essence of a small UNIX-style operating
system complete with multi-user environment, time-sharing, and file I/O.
The second strand studies continuation passing style (CPS) and abstract machine
semantics, which are foundational techniques that admit a unified basis for implementing deep, shallow, and parameterised effect handlers in the same environment. The
CPS translation is obtained through a series of refinements of a basic first-order CPS
translation for a fine-grain call-by-value language into an untyped language. Each refinement moves toward a more intensional representation of continuations eventually
arriving at the notion of generalised continuation, which admit simultaneous support for
deep, shallow, and parameterised handlers. The initial refinement adds support for deep
handlers by representing stacks of continuations and handlers as a curried sequence of
arguments. The image of the resulting translation is not properly tail-recursive, meaning some function application terms do not appear in tail position. To rectify this the
CPS translation is refined once more to obtain an uncurried representation of stacks
of continuations and handlers. Finally, the translation is made higher-order in order to
contract administrative redexes at translation time. The generalised continuation representation is used to construct an abstract machine that provide simultaneous support for
deep, shallow, and parameterised effect handlers. kinds of effect handlers.
The third strand explores the expressiveness of effect handlers. First, I show that
deep, shallow, and parameterised notions of handlers are interdefinable by way of typed
macro-expressiveness, which provides a syntactic notion of expressiveness that affirms
the existence of encodings between handlers, but it provides no information about the
computational content of the encodings. Second, using the semantic notion of expressiveness I show that for a class of programs a programming language with first-class
control (e.g. effect handlers) admits asymptotically faster implementations than possible in a language without first-class control
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