arXiv subjects

Carlos E. González-Guillén

Publications and source records attributed to Carlos E. González-Guillén.

11 recordsLinked to original sources

arXiv2025

Enhancing reliability in prediction intervals using point forecasters: Heteroscedastic Quantile Regression and Width-Adaptive Conformal Inference

Constructing prediction intervals for time series forecasting is challenging, particularly when practitioners rely solely on point forecasts. While previous research has focused on creating increasingly efficient intervals, we argue that standard measures alone are inadequate. Beyond efficiency, prediction intervals must adapt their width based on the difficulty of the prediction while preserving coverage regardless of complexity. To address these issues, we propose combining Heteroscedastic Quantile Regression (HQR) with Width-Adaptive Conformal Inference (WACI). This integrated procedure guarantees theoretical coverage and enables interval widths to vary with predictive uncertainty. We assess its performance using both a synthetic example and a real world Electricity Price Forecasting scenario. Our results show that this combined approach meets or surpasses typical benchmarks for validity and efficiency, while also fulfilling important yet often overlooked practical requirements.

stat.ME↗

arXiv2024

Privacy-preserving machine learning with tensor networks

Tensor networks, widely used for providing efficient representations of low-energy states of local quantum many-body systems, have been recently proposed as machine learning architectures which could present advantages with respect to traditional ones. In this work we show that tensor network architectures have especially prospective properties for privacy-preserving machine learning, which is important in tasks such as the processing of medical records. First, we describe a new privacy vulnerability that is present in feedforward neural networks, illustrating it in synthetic and real-world datasets. Then, we develop well-defined conditions to guarantee robustness to such vulnerability, which involve the characterization of models equivalent under gauge symmetry. We rigorously prove that such conditions are satisfied by tensor-network architectures. In doing so, we define a novel canonical form for matrix product states, which has a high degree of regularity and fixes the residual gauge that is left in the canonical forms based on singular value decompositions. We supplement the analytical findings with practical examples where matrix product states are trained on datasets of medical records, which show large reductions on the probability of an attacker extracting information about the training dataset from the model's parameters. Given the growing expertise in training tensor-network architectures, these results imply that one may not have to be forced to make a choice between accuracy in prediction and ensuring the privacy of the information processed.

cs.CR↗

arXiv2024

An adaptive standardisation methodology for Day-Ahead electricity price forecasting

The study of Day-Ahead prices in the electricity market is one of the most popular problems in time series forecasting. Previous research has focused on employing increasingly complex learning algorithms to capture the sophisticated dynamics of the market. However, there is a threshold where increased complexity fails to yield substantial improvements. In this work, we propose an alternative approach by introducing an adaptive standardisation to mitigate the effects of dataset shifts that commonly occur in the market. By doing so, learning algorithms can prioritize uncovering the true relationship between the target variable and the explanatory variables. We investigate five distinct markets, including two novel datasets, previously unexplored in the literature. These datasets provide a more realistic representation of the current market context, that conventional datasets do not show. The results demonstrate a significant improvement across all five markets using the widely accepted learning algorithms in the literature (LEAR and DNN). In particular, the combination of the proposed methodology with the methodology previously presented in the literature obtains the best results. This significant advancement unveils new lines of research in this field, highlighting the potential of adaptive transformations in enhancing the performance of forecasting models.

stat.AP↗

arXiv2023

A feature selection method based on Shapley values robust to concept shift in regression

Feature selection is one of the most relevant processes in any methodology for creating a statistical learning model. Usually, existing algorithms establish some criterion to select the most influential variables, discarding those that do not contribute to the model with any relevant information. This methodology makes sense in a static situation where the joint distribution of the data does not vary over time. However, when dealing with real data, it is common to encounter the problem of the dataset shift and, specifically, changes in the relationships between variables (concept shift). In this case, the influence of a variable cannot be the only indicator of its quality as a regressor of the model, since the relationship learned in the training phase may not correspond to the current situation. In tackling this problem, our approach establishes a direct relationship between the Shapley values and prediction errors, operating at a more local level to effectively detect the individual biases introduced by each variable. The proposed methodology is evaluated through various examples, including synthetic scenarios mimicking sudden and incremental shift situations, as well as two real-world cases characterized by concept shifts. Additionally, we perform three analyses of standard situations to assess the algorithm's robustness in the absence of shifts. The results demonstrate that our proposed algorithm significantly outperforms state-of-the-art feature selection methods in concept shift scenarios, while matching the performance of existing methodologies in static situations.

stat.ML↗

arXiv2022

Mixing and localisation in random time-periodic quantum circuits of Clifford unitaries

How much does local and time-periodic dynamics resemble a random unitary? In the present work we address this question by using the Clifford formalism from quantum computation. We analyse a Floquet model with disorder, characterised by a family of local, time-periodic, random quantum circuits in one spatial dimension. We observe that the evolution operator enjoys an extra symmetry at times that are a half-integer multiple of the period. With this we prove that after the scrambling time, namely when any initial perturbation has propagated throughout the system, the evolution operator cannot be distinguished from a (Haar) random unitary when all qubits are measured with Pauli operators. This indistinguishability decreases as time goes on, which is in high contrast to the more studied case of (time-dependent) random circuits. We also prove that the evolution of Pauli operators displays a form of mixing. These results require the dimension of the local subsystem to be large. In the opposite regime our system displays a novel form of localisation, produced by the appearance of effective one-sided walls, which prevent perturbations from crossing the wall in one direction but not the other.

quant-ph↗

arXiv2021

Quantum Private Broadcasting

In Private Broadcasting, a single plaintext is broadcast to multiple recipients in an encrypted form, such that each recipient can decrypt locally. When the message is classical, a straightforward solution is to encrypt the plaintext with a single key shared among all parties, and to send to each recipient a copy of the ciphertext. Surprisingly, the analogous method is insufficient in the case where the message is quantum (i.e. in Quantum Private Broadcasting (QPB)). In this work, we give three solutions to $t$-recipient Quantum Private Broadcasting ($t$-QPB) and compare them in terms of key lengths. The first method is the independent encryption with the quantum one-time pad, which requires a key linear in the number of recipients, $t$. We show that the key length can be decreased to be logarithmic in $t$ by using unitary $t$-designs. Our main contribution is to show that this can be improved to a key length that is logarithmic in the dimension of the symmetric subspace, using a new concept that we define of symmetric unitary $t$-designs, that may be of independent interest.

quant-ph↗

arXiv2020

Concerning Quantum Identification Without Entanglement

Identification schemes are interactive protocols typically involving two parties, a prover, who wants to provide evidence of his or her identity and a verifier, who checks the provided evidence and decide whether it comes or not from the intended prover. In this paper, we comment on a recent proposal for quantum identity authentication from Zawadzki, and give a concrete attack upholding theoretical impossibility results from Lo and Buhrman et al. More precisely, we show that using a simple strategyan adversary may indeed obtain non-negligible information on the shared identification secret. While the security of a quantum identity authentication scheme is not formally defined in [1], it is clear that such a definition should somehow imply that an external entity may gain no information on the shared identification scheme (even if he actively participates injecting messages in a protocol execution, which is not assumed in our attack strategy).

quant-ph↗

arXiv2018

On the spectral gap of random quantum channels

In this work, we prove a lower bound on the difference between the first and second singular values of quantum channels induced by random isometries, that is tight in the scaling of the number of Kraus operators. This allows us to give an upper bound on the difference between the first and second largest (in modulus) eigenvalues of random channels with same large input and output dimensions for finite number of Kraus operators $k\geq 169$. Moreover, we show that these random quantum channels are quantum expanders, answering a question posed by Hastings. As an application, we show that ground states of infinite 1D spin chains, which are well-approximated by matrix product states, fulfill a principle of maximum entropy.

quant-ph↗

arXiv2018

History-state Hamiltonians are critical

All Hamiltonian complexity results to date have been proven by constructing a local Hamiltonian whose ground state -- or at least some low-energy state -- is a "computational history state", encoding a quantum computation as a superposition over the history of the computation. We prove that all history-state Hamiltonians must be critical. More precisely, for any circuit-to-Hamiltonian mapping that maps quantum circuits to local Hamiltonians with low-energy history states, there is an increasing sequence of circuits that maps to a growing sequence of Hamiltonians with spectral gap closing at least as fast as O(1/n) with the number of qudits n in the circuit. This result holds for very general notions of history state, and also extends to quasi-local Hamiltonians with exponentially-decaying interactions. This suggests that QMA-hardness for gapped Hamiltonians (and also BQP-completeness of adiabatic quantum computation with constant gap) either require techniques beyond history state constructions. Or gapped Hamiltonians cannot be QMA-hard (respectively, BQP-complete).

quant-ph↗

arXiv2016

Sampling quantum nonlocal correlations with high probability

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form $γ=(\langle u_i,v_j\rangle)_{i,j=1}^n$, where the vectors $u_i$ and $v_j$ are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of $α=\frac{m}{n}$, where the previous vectors are sampled according to the Haar measure in the unit sphere of $\mathbb R^m$. In particular, we prove the existence of an $α_0>0$ such that if $α\leq α_0$, $γ$ is nonlocal with probability tending to $1$ as $n\rightarrow \infty$, while for $α> 2$, $γ$ is local with probability tending to $1$ as $n\rightarrow \infty$.

quant-ph↗

arXiv2016

Euclidean distance between Haar orthogonal and gaussian matrices

In this work we study a version of the general question of how well a Haar distributed orthogonal matrix can be approximated by a random gaussian matrix. Here, we consider a gaussian random matrix $Y_n$ of order $n$ and apply to it the Gram-Schmidt orthonormalization procedure by columns to obtain a Haar distributed orthogonal matrix $U_n$. If $F_i^m$ denotes the vector formed by the first $m$-coordinates of the $i$th row of $Y_n-\sqrt{n}U_n$ and $α=\frac{m}{n}$, our main result shows that the euclidean norm of $F_i^m$ converges exponentially fast to $\sqrt{ \left(2-\frac{4}{3} \frac{(1-(1 -α)^{3/2})}α\right)m}$, up to negligible terms. To show the extent of this result, we use it to study the convergence of the supremum norm $ε_n(m)=\sup_{1\leq i \leq n, 1\leq j \leq m} |y_{i,j}- \sqrt{n}u_{i,j}|$ and we find a coupling that improves by a factor $\sqrt{2}$ the recently proved best known upper bound of $ε_n(m)$. Applications of our results to Quantum Information Theory are also explained.

math.PR↗