arXiv subjects

Florian Huber

Publications and source records attributed to Florian Huber.

At least 37 records · Page 2Linked to original sources

arXiv2024

Large-scale quantum reservoir learning with an analog quantum computer

Quantum machine learning has gained considerable attention as quantum technology advances, presenting a promising approach for efficiently learning complex data patterns. Despite this promise, most contemporary quantum methods require significant resources for variational parameter optimization and face issues with vanishing gradients, leading to experiments that are either limited in scale or lack potential for quantum advantage. To address this, we develop a general-purpose, gradient-free, and scalable quantum reservoir learning algorithm that harnesses the quantum dynamics of neutral-atom analog quantum computers to process data. We experimentally implement the algorithm, achieving competitive performance across various categories of machine learning tasks, including binary and multi-class classification, as well as timeseries prediction. Effective and improving learning is observed with increasing system sizes of up to 108 qubits, demonstrating the largest quantum machine learning experiment to date. We further observe comparative quantum kernel advantage in learning tasks by constructing synthetic datasets based on the geometric differences between generated quantum and classical data kernels. Our findings demonstrate the potential of utilizing classically intractable quantum correlations for effective machine learning. We expect these results to stimulate further extensions to different quantum hardware and machine learning paradigms, including early fault-tolerant hardware and generative machine learning tasks.

quant-ph↗

arXiv2024

Quantum quench dynamics as a shortcut to adiabaticity

The ability to efficiently prepare ground states of quantum Hamiltonians via adiabatic protocols is typically limited by the smallest energy gap encountered during the quantum evolution. This presents a key obstacle for quantum simulation and realizations of adiabatic quantum algorithms in large systems, particularly when the adiabatic gap vanishes exponentially with system size. Using QuEra's Aquila programmable quantum simulator based on Rydberg atom arrays, we experimentally demonstrate a method to circumvent such limitations. Specifically, we develop and test a "sweep-quench-sweep" quantum algorithm in which the incorporation of a quench step serves as a remedy to the diverging adiabatic timescale. These quenches introduce a macroscopic reconfiguration between states separated by an extensively large Hamming distance, akin to quantum many-body scars. Our experiments show that this approach significantly outperforms the adiabatic algorithm, illustrating that such quantum quench algorithms can provide a shortcut to adiabaticity for large-scale many-body quantum systems.

quant-ph↗

arXiv2024

Polynomial interacting particle systems and non-linear SPDEs for market capitalization curves

Motivated by the robustness of the capital distribution curves, we study the behavior of a certain polynomial equity market model as the number of companies goes to infinity. More precisely, we extend volatility-stabilized market models introduced by Fernholz et al. by allowing for a common noise term such that the models remain polynomial. As the number of companies approaches infinity, we show that the limit of the empirical measure of the $N$-company system converges to the unique solution of a degenerate, non-linear SPDE. The obtained limit also has a representation as the conditional probability of the solution to a certain McKean-Vlasov SDE. Together with its conditional, this is again a polynomial process for which we can prove pathwise uniqueness as well as regularity properties for the marginal densities. We also provide conditional propagation of chaos results and numerical implementations of the particle system as well as its limiting equations.

math.PR↗

arXiv2024

Bayesian Neural Networks for Macroeconomic Analysis

Macroeconomic data is characterized by a limited number of observations (small T), many time series (big K) but also by featuring temporal dependence. Neural networks, by contrast, are designed for datasets with millions of observations and covariates. In this paper, we develop Bayesian neural networks (BNNs) that are well-suited for handling datasets commonly used for macroeconomic analysis in policy institutions. Our approach avoids extensive specification searches through a novel mixture specification for the activation function that appropriately selects the form of nonlinearities. Shrinkage priors are used to prune the network and force irrelevant neurons to zero. To cope with heteroskedasticity, the BNN is augmented with a stochastic volatility model for the error term. We illustrate how the model can be used in a policy institution by first showing that our different BNNs produce precise density forecasts, typically better than those from other machine learning methods. Finally, we showcase how our model can be used to recover nonlinearities in the reaction of macroeconomic aggregates to financial shocks.

econ.EM↗

arXiv2024

Sophisticated and small versus simple and sizeable: When does it pay off to introduce drifting coefficients in Bayesian VARs?

We assess the relationship between model size and complexity in the time-varying parameter VAR framework via thorough predictive exercises for the Euro Area, the United Kingdom and the United States. It turns out that sophisticated dynamics through drifting coefficients are important in small data sets, while simpler models tend to perform better in sizeable data sets. To combine the best of both worlds, novel shrinkage priors help to mitigate the curse of dimensionality, resulting in competitive forecasts for all scenarios considered. Furthermore, we discuss dynamic model selection to improve upon the best performing individual model for each point in time.

stat.ME↗

arXiv2024

On Convolutional Vision Transformers for Yield Prediction

While a variety of methods offer good yield prediction on histogrammed remote sensing data, vision Transformers are only sparsely represented in the literature. The Convolution vision Transformer (CvT) is being tested to evaluate vision Transformers that are currently achieving state-of-the-art results in many other vision tasks. CvT combines some of the advantages of convolution with the advantages of dynamic attention and global context fusion of Transformers. It performs worse than widely tested methods such as XGBoost and CNNs, but shows that Transformers have potential to improve yield prediction.

cs.CV↗

arXiv2024

Nowcasting economic activity in European regions using a mixed-frequency dynamic factor model

Timely information about the state of regional economies can be essential for planning, implementing and evaluating locally targeted economic policies. However, European regional accounts for output are published at an annual frequency and with a two-year delay. To obtain robust and more timely measures in a computationally efficient manner, we propose a mixed-frequency dynamic factor model that accounts for national information to produce high-frequency estimates of the regional gross value added (GVA). We show that our model produces reliable nowcasts of GVA in 162 regions across 12 European countries.

econ.EM↗

arXiv2024

Probing quantum floating phases in Rydberg atom arrays

The floating phase, a critical incommensurate phase, has been theoretically predicted as a potential intermediate phase between crystalline ordered and disordered phases. In this study, we investigate the different quantum phases that arise in ladder arrays comprising up to 92 neutral-atom qubits and experimentally observe the emergence of the quantum floating phase. We analyze the site-resolved Rydberg state densities and the distribution of state occurrences. The site-resolved measurement reveals the formation of domain walls within the commensurate ordered phase, which subsequently proliferate and give rise to the floating phase with incommensurate quasi-long-range order. By analyzing the Fourier spectra of the Rydberg density-density correlations, we observe clear signatures of the incommensurate wave order of the floating phase. Furthermore, as the experimental system sizes increase, we show that the wave vectors approach a continuum of values incommensurate with the lattice. Our work motivates future studies to further explore the nature of commensurate-incommensurate phase transitions and their non-equilibrium physics.

quant-ph↗

arXiv2023

Bayesian Nonlinear Regression using Sums of Simple Functions

This paper proposes a new Bayesian machine learning model that can be applied to large datasets arising in macroeconomics. Our framework sums over many simple two-component location mixtures. The transition between components is determined by a logistic function that depends on a single threshold variable and two hyperparameters. Each of these individual models only accounts for a minor portion of the variation in the endogenous variables. But many of them are capable of capturing arbitrary nonlinear conditional mean relations. Conjugate priors enable fast and efficient inference. In simulations, we show that our approach produces accurate point and density forecasts. In a real-data exercise, we forecast US macroeconomic aggregates and consider the nonlinear effects of financial shocks in a large-scale nonlinear VAR.

econ.EM↗

arXiv2023

Predictive Density Combination Using a Tree-Based Synthesis Function

Bayesian predictive synthesis (BPS) provides a method for combining multiple predictive distributions based on agent/expert opinion analysis theory and encompasses a range of existing density forecast pooling methods. The key ingredient in BPS is a ``synthesis'' function. This is typically specified parametrically as a dynamic linear regression. In this paper, we develop a nonparametric treatment of the synthesis function using regression trees. We show the advantages of our tree-based approach in two macroeconomic forecasting applications. The first uses density forecasts for GDP growth from the euro area's Survey of Professional Forecasters. The second combines density forecasts of US inflation produced by many regression models involving different predictors. Both applications demonstrate the benefits -- in terms of improved forecast accuracy and interpretability -- of modeling the synthesis function nonparametrically.

econ.EM↗

arXiv2023

Comment on "Photons can tell 'contradictory' answer about where they have been''

Yuan and Feng [Eur. Phys. J. Plus 138:70, 2023] recently proposed a modification of the nested Mach-Zehnder interferometer experiment performed by Danan et al. [Phys. Rev. Lett. 111:240402, 2013] and argued that photons give "contradictory" answers about where they have been, when traces are locally imprinted on them in different ways. They concluded that their results are comprehensible from what they call the "three-path interference viewpoint", but difficult to explain from the "discontinuous trajectory" viewpoint advocated by Danan et al. We argue that the weak trace approach (the basis of the "discontinuous trajectory" viewpoint) provides a consistent explanation of the Yuan-Feng experiment. The contradictory messages of the photons are just another example of photons lying about where they have been when the experimental method of Danan et al. is applied in an inappropriate setup.

quant-ph↗

arXiv2023

Nonlinearities in Macroeconomic Tail Risk through the Lens of Big Data Quantile Regressions

Modeling and predicting extreme movements in GDP is notoriously difficult and the selection of appropriate covariates and/or possible forms of nonlinearities are key in obtaining precise forecasts. In this paper, our focus is on using large datasets in quantile regression models to forecast the conditional distribution of US GDP growth. To capture possible non-linearities, we include several nonlinear specifications. The resulting models will be huge dimensional and we thus rely on a set of shrinkage priors. Since Markov Chain Monte Carlo estimation becomes slow in these dimensions, we rely on fast variational Bayes approximations to the posterior distribution of the coefficients and the latent states. We find that our proposed set of models produces precise forecasts. These gains are especially pronounced in the tails. Using Gaussian processes to approximate the nonlinear component of the model further improves the good performance, in particular in the right tail.

econ.EM↗

arXiv2023

Bayesian Forecasting in Economics and Finance: A Modern Review

The Bayesian statistical paradigm provides a principled and coherent approach to probabilistic forecasting. Uncertainty about all unknowns that characterize any forecasting problem -- model, parameters, latent states -- is able to be quantified explicitly, and factored into the forecast distribution via the process of integration or averaging. Allied with the elegance of the method, Bayesian forecasting is now underpinned by the burgeoning field of Bayesian computation, which enables Bayesian forecasts to be produced for virtually any problem, no matter how large, or complex. The current state of play in Bayesian forecasting in economics and finance is the subject of this review. The aim is to provide the reader with an overview of modern approaches to the field, set in some historical context; and with sufficient computational detail given to assist the reader with implementation.

econ.EM↗

arXiv2023

Aquila: QuEra's 256-qubit neutral-atom quantum computer

The neutral-atom quantum computer "Aquila" is QuEra's latest device available through the Braket cloud service on Amazon Web Services (AWS). Aquila is a "field-programmable qubit array" (FPQA) operated as an analog Hamiltonian simulator on a user-configurable architecture, executing programmable coherent quantum dynamics on up to 256 neutral-atom qubits. This whitepaper serves as an overview of Aquila and its capabilities: how it works under the hood, key performance benchmarks, and examples that demonstrate some quintessential applications. This includes an overview of neutral-atom quantum computing, as well as five examples of increasing complexity from single-qubit dynamics to combinatorial optimization, implemented on Aquila. This whitepaper is intended for readers who are interested in learning more about neutral-atom quantum computing, as a guide for those who are ready to start using Aquila, and as a reference point for its performance as an analog quantum computer.

quant-ph↗

arXiv2023

Fast and Order-invariant Inference in Bayesian VARs with Non-Parametric Shocks

The shocks which hit macroeconomic models such as Vector Autoregressions (VARs) have the potential to be non-Gaussian, exhibiting asymmetries and fat tails. This consideration motivates the VAR developed in this paper which uses a Dirichlet process mixture (DPM) to model the shocks. However, we do not follow the obvious strategy of simply modeling the VAR errors with a DPM since this would lead to computationally infeasible Bayesian inference in larger VARs and potentially a sensitivity to the way the variables are ordered in the VAR. Instead we develop a particular additive error structure inspired by Bayesian nonparametric treatments of random effects in panel data models. We show that this leads to a model which allows for computationally fast and order-invariant inference in large VARs with nonparametric shocks. Our empirical results with nonparametric VARs of various dimensions shows that nonparametric treatment of the VAR errors is particularly useful in periods such as the financial crisis and the pandemic.

econ.EM↗

arXiv2023

Dynamic Shrinkage Priors for Large Time-varying Parameter Regressions using Scalable Markov Chain Monte Carlo Methods

Time-varying parameter (TVP) regression models can involve a huge number of coefficients. Careful prior elicitation is required to yield sensible posterior and predictive inferences. In addition, the computational demands of Markov Chain Monte Carlo (MCMC) methods mean their use is limited to the case where the number of predictors is not too large. In light of these two concerns, this paper proposes a new dynamic shrinkage prior which reflects the empirical regularity that TVPs are typically sparse (i.e. time variation may occur only episodically and only for some of the coefficients). A scalable MCMC algorithm is developed which is capable of handling very high dimensional TVP regressions or TVP Vector Autoregressions. In an exercise using artificial data we demonstrate the accuracy and computational efficiency of our methods. In an application involving the term structure of interest rates in the eurozone, we find our dynamic shrinkage prior to effectively pick out small amounts of parameter change and our methods to forecast well.

econ.EM↗

arXiv2023

Bayesian Modeling of TVP-VARs Using Regression Trees

In light of widespread evidence of parameter instability in macroeconomic models, many time-varying parameter (TVP) models have been proposed. This paper proposes a nonparametric TVP-VAR model using Bayesian additive regression trees (BART) that models the TVPs as an unknown function of effect modifiers. The novelty of this model arises from the fact that the law of motion driving the parameters is treated nonparametrically. This leads to great flexibility in the nature and extent of parameter change, both in the conditional mean and in the conditional variance. Parsimony is achieved through adopting nonparametric factor structures and use of shrinkage priors. In an application to US macroeconomic data, we illustrate the use of our model in tracking both the evolving nature of the Phillips curve and how the effects of business cycle shocks on inflation measures vary nonlinearly with changes in the effect modifiers.

econ.EM↗

arXiv2023

Grouping Shapley Value Feature Importances of Random Forests for explainable Yield Prediction

Explainability in yield prediction helps us fully explore the potential of machine learning models that are already able to achieve high accuracy for a variety of yield prediction scenarios. The data included for the prediction of yields are intricate and the models are often difficult to understand. However, understanding the models can be simplified by using natural groupings of the input features. Grouping can be achieved, for example, by the time the features are captured or by the sensor used to do so. The state-of-the-art for interpreting machine learning models is currently defined by the game-theoretic approach of Shapley values. To handle groups of features, the calculated Shapley values are typically added together, ignoring the theoretical limitations of this approach. We explain the concept of Shapley values directly computed for predefined groups of features and introduce an algorithm to compute them efficiently on tree structures. We provide a blueprint for designing swarm plots that combine many local explanations for global understanding. Extensive evaluation of two different yield prediction problems shows the worth of our approach and demonstrates how we can enable a better understanding of yield prediction models in the future, ultimately leading to mutual enrichment of research and application.

cs.LG↗