Related papers: Quantum Classification Outside the Promised Class
We initiate the study of a new model of query complexity of Boolean functions where, in addition to 0 and 1, the oracle can answer queries with ``unknown''. The query algorithm is expected to output the function value if it can be…
Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…
Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…
The estimation of the guessing probability has paramount importance in quantum cryptographic processes. It can also be used as a witness for nonlocal correlations. In most of the studied scenarios, estimating the guessing probability…
Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…
Quantum information processing offers promising advances for a wide range of fields and applications, provided that we can efficiently assess the performance of the control applied in candidate systems. That is, we must be able to determine…
By using a new way to encode Boolean functions in a reversible gate, an algorithm is developed in quantum computing over Z_2, symbolized QC/2, (as opposed to QC over C) that needs only one function evaluation to solve the Grover Database…
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of…
We study minimum-error identification of an unknown single-bit Boolean function given black-box (oracle) access with one allowed query. Rather than stopping at an abstract optimal measurement, we give a fully constructive solution: an…
There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a…
Machine learning, a branch of artificial intelligence, learns from previous experience to optimize performance, which is ubiquitous in various fields such as computer sciences, financial analysis, robotics, and bioinformatics. A challenge…
Pattern recognition is a central topic in Learning Theory with numerous applications such as voice and text recognition, image analysis, computer diagnosis. The statistical set-up in classification is the following: we are given an i.i.d.…
Consider a database most of whose entries are marked but the precise fraction of marked entries is not known. What is known is that the fraction of marked entries is 1-X, where X is a random variable that is uniformly distributed in the…
It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these…
We propose a quantum algorithm for `extremal learning', which is the process of finding the input to a hidden function that extremizes the function output, without having direct access to the hidden function, given only partial input-output…
Feature selection is a common step in many ranking, classification, or prediction tasks and serves many purposes. By removing redundant or noisy features, the accuracy of ranking or classification can be improved and the computational cost…
The hybrid quantum-classical learning scheme provides a prominent way to achieve quantum advantages on near-term quantum devices. A concrete example towards this goal is the quantum neural network (QNN), which has been developed to…
Learning to quantify (a.k.a.\ quantification) is a task concerned with training unbiased estimators of class prevalence via supervised learning. This task originated with the observation that "Classify and Count" (CC), the trivial method of…
Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…