Related papers: Operator on Operator Regression in Quantum Probabi…
It is shown that an operator can be defined in the abstract space of random matrices ensembles whose matrix elements statistical distribution simulates the behavior of the distribution found in real physical systems. It is found that the…
This paper is concerned with inference about low-dimensional components of a high-dimensional parameter vector $\beta^0$ which is identified through instrumental variables. We allow for eigenvalues of the expected outer product of included…
This paper studies sparse covariance operator estimation for nonstationary processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covariance operator estimator that adaptively thresholds the…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
We conduct a spectral analysis of the difference quotient operator $Q^u_\zeta$, associated with a boundary point $\zeta \in \partial \mathbb{D}$, on the model space $K_u$. We describe the operator's spectrum and provide both upper and lower…
We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels…
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…
Many quantum algorithms involve the evaluation of expectation values. Optimal strategies for estimating a single expectation value are known, requiring a number of state preparations that scales with the target error $\varepsilon$ as…
Quantile Regression (QR) can be used to estimate aleatoric uncertainty in deep neural networks and can generate prediction intervals. Quantifying uncertainty is particularly important in critical applications such as clinical diagnosis,…
There are two major approaches to building good machine learning algorithms: feeding lots of data into large models, or picking a model class with an ''inductive bias'' that suits the structure of the data. When taking the second approach…
We develop a unified operator framework for scalar, multivariate, and functional regression based on integral operators defined with respect to general measures. Within this framework, classical regression models, including…
Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
Variational quantum circuits have become a widely used tool for performing quantum machine learning (QML) tasks on labeled quantum states. In some specific tasks or for specific variational ans\"atze, one may perform measurements on a…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
Variational quantum algorithms have gained attention as early applications of quantum computers for learning tasks. In the context of supervised learning, most of the works that tackle classification problems with parameterized quantum…
A new form of ML knowledge representation with high generalization power is developed and implemented numerically. Initial $\mathit{IN}$ attributes and $\mathit{OUT}$ class label are transformed into the corresponding Hilbert spaces by…
We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are…
What is the observer's role in quantum measurement? Obviously, observers prepare the apparatus, observe and interpret the measured results. Although the observer will have a certain influence on the measurement results by setting up the…
The evaluation of uncertainties in quantum measurements is problematic since the correct value of an observable between state preparation and measurement is experimentally inaccessible. In Ozawa's formulation of uncertainty relations for…