Cloud storage systems provide several benefits, such as scalable storage capacity, cost efficiency with pay-as-you-go pricing models, easy access from any location with an internet connection, and robust data backup options. These advantages drive the growing popularity of cloud storage, resulting in a rapid increase in the volume of data stored on the cloud. Deduplication is an effective data management technique used in these systems to reduce storage costs and enhance efficiency through the elimination of redundant data. However, in a deduplication system, a hash digest, i.e., a small piece of information, is used as ownership proof of the entire file. Therefore, a malicious user can gain access to a sensitive file already stored on the cloud by obtaining and presenting the hash digest of that file. On the other hand, data stored in the cloud may be susceptible to loss or damage due to various accidental or intentional reasons. Hence, there is a need for an ownership verification protocol where both the user and server can verify each other’s file ownership without revealing details about the file. Some existing state-of-the-art schemes consider the server as a trusted entity and focus solely on verifying the ownership of the user, while others emphasize bidirectional ownership verification but do not incorporate obliviousness in their solutions. In this paper, we propose a novel bidirectional and oblivious ownership verification scheme for deduplication systems. We cryptographically prove that adversaries lacking complete ownership of the file, cannot successfully pass ownership verification with non-negligible probability. Additionally, we show that adversaries cannot gain any knowledge about the file through the ownership verification process. We implement our scheme in two real cloud scenarios and analyze performance compared to the recent state-of-the-art schemes. The experimental results demonstrate that our approach incurs moderate computational, communication, storage, and energy overheads while achieving ownership authentication and maintaining obliviousness in deduplicated cloud storage systems.

We analyze the statistical properties of generalized cross-validation (GCV) and leave-one-out cross-validation (LOOCV) applied to early-stopped gradient descent (GD) in high-dimensional least squares regression. We prove that GCV is generically inconsistent as an estimator of the prediction risk of early-stopped GD, even for a well-specified linear model with isotropic features. In contrast, we show that LOOCV converges uniformly along the GD trajectory to the prediction risk. Our theory requires only mild assumptions on the data distribution and does not require the underlying regression function to be linear. Furthermore, by leveraging the individual LOOCV errors, we construct consistent estimators for the entire prediction error distribution along the GD trajectory and consistent estimators for a wide class of error functionals. This in particular enables the construction of pathwise prediction intervals based on GD iterates that have asymptotically correct nominal coverage conditional on the training data.

How can we precisely estimate a large language model's (LLM) accuracy on questions belonging to a specific topic within a larger questionanswering dataset?The standard direct estimator, which averages the model's accuracy on the questions in each subgroup, may exhibit high variance for subgroups (topics) with small sample sizes.Synthetic regression modeling, which leverages the model's accuracy on questions about other topics, may yield biased estimates that are too unreliable for large subgroups.We prescribe a simple yet effective solution: an empirical Bayes (EB) estimator that balances direct and regression estimates for each subgroup separately, improving the precision of subgroup-level estimates of model performance.Our experiments on multiple datasets show that this approach consistently provides more precise estimates of the LLM performance compared to the direct and regression approaches, achieving substantial reductions in the mean squared error.Confidence intervals for EB estimates also have nearnominal coverage and are narrower compared to those for the direct estimator.Additional experiments on tabular and vision data validate the benefits of this EB approach.

We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching parameters. Our results hold for a broad class of asymptotically free sketches under very mild data assumptions. For squared prediction risk, we provide a decomposition into an unsketched equivalent implicit ridge bias and a sketching-based variance, and prove that the risk can be globally optimized by only tuning sketch size in infinite ensembles. For general subquadratic prediction risk functionals, we extend GCV to construct consistent risk estimators, and thereby obtain distributional convergence of the GCV-corrected predictions in Wasserstein-2 metric. This in particular allows construction of prediction intervals with asymptotically correct coverage conditional on the training data. We also propose an "ensemble trick" whereby the risk for unsketched ridge regression can be efficiently estimated via GCV using small sketched ridge ensembles. We empirically validate our theoretical results using both synthetic and real large-scale datasets with practical sketches including CountSketch and subsampled randomized discrete cosine transforms.

We study the behavior of optimal ridge regularization and optimal ridge risk for out-of-distribution prediction, where the test distribution deviates arbitrarily from the train distribution. We establish general conditions that determine the sign of the optimal regularization level under covariate and regression shifts. These conditions capture the alignment between the covariance and signal structures in the train and test data and reveal stark differences compared to the in-distribution setting. For example, a negative regularization level can be optimal under covariate shift or regression shift, even when the training features are isotropic or the design is underparameterized. Furthermore, we prove that the optimally tuned risk is monotonic in the data aspect ratio, even in the out-of-distribution setting and when optimizing over negative regularization levels. In general, our results do not make any modeling assumptions for the train or the test distributions, except for moment bounds, and allow for arbitrary shifts and the widest possible range of (negative) regularization levels.

We study the implicit regularization effects induced by (observation) weighting of pretrained features. For weight and feature matrices of bounded operator norms that are infinitesimally free with respect to (normalized) trace functionals, we derive equivalence paths connecting different weighting matrices and ridge regularization levels. Specifically, we show that ridge estimators trained on weighted features along the same path are asymptotically equivalent when evaluated against test vectors of bounded norms. These paths can be interpreted as matching the effective degrees of freedom of ridge estimators fitted with weighted features. For the special case of subsampling without replacement, our results apply to independently sampled random features and kernel features and confirm recent conjectures (Conjectures 7 and 8) of the authors on the existence of such paths in Patil and Du (2023). We also present an additive risk decomposition for ensembles of weighted estimators and show that the risks are equivalent along the paths when the ensemble size goes to infinity. As a practical consequence of the path equivalences, we develop an efficient cross-validation method for tuning and apply it to subsampled pretrained representations across several models (e.g., ResNet-50) and datasets (e.g., CIFAR-100).

We study subsampling-based ridge ensembles in the proportional asymptotics regime, where the feature size grows proportionally with the sample size such that their ratio converges to a constant. By analyzing the squared prediction risk of ridge ensembles as a function of the explicit penalty $\lambda$ and the limiting subsample aspect ratio $\phi_s$ (the ratio of the feature size to the subsample size), we characterize contours in the $(\lambda, \phi_s)$-plane at any achievable risk. As a consequence, we prove that the risk of the optimal full ridgeless ensemble (fitted on all possible subsamples) matches that of the optimal ridge predictor. In addition, we prove strong uniform consistency of generalized cross-validation (GCV) over the subsample sizes for estimating the prediction risk of ridge ensembles. This allows for GCV-based tuning of full ridgeless ensembles without sample splitting and yields a predictor whose risk matches optimal ridge risk.

We establish precise structural and risk equivalences between subsampling and ridge regularization for ensemble ridge estimators. Specifically, we prove that linear and quadratic functionals of subsample ridge estimators, when fitted with different ridge regularization levels $\lambda$ and subsample aspect ratios $\psi$, are asymptotically equivalent along specific paths in the $(\lambda,\psi)$-plane (where $\psi$ is the ratio of the feature dimension to the subsample size). Our results only require bounded moment assumptions on feature and response distributions and allow for arbitrary joint distributions. Furthermore, we provide a data-dependent method to determine the equivalent paths of $(\lambda,\psi)$. An indirect implication of our equivalences is that optimally tuned ridge regression exhibits a monotonic prediction risk in the data aspect ratio. This resolves a recent open problem raised by Nakkiran et al. for general data distributions under proportional asymptotics, assuming a mild regularity condition that maintains regression hardness through linearized signal-to-noise ratios.

Bagging is a commonly used ensemble technique in statistics and machine learning to improve the performance of prediction procedures. In this paper, we study the prediction risk of variants of bagged predictors under the proportional asymptotics regime, in which the ratio of the number of features to the number of observations converges to a constant. Specifically, we propose a general strategy to analyze the prediction risk under squared error loss of bagged predictors using classical results on simple random sampling. Specializing the strategy, we derive the exact asymptotic risk of the bagged ridge and ridgeless predictors with an arbitrary number of bags under a well-specified linear model with arbitrary feature covariance matrices and signal vectors. Furthermore, we prescribe a generic cross-validation procedure to select the optimal subsample size for bagging and discuss its utility to eliminate the non-monotonic behavior of the limiting risk in the sample size (i.e., double or multiple descents). In demonstrating the proposed procedure for bagged ridge and ridgeless predictors, we thoroughly investigate the oracle properties of the optimal subsample size and provide an in-depth comparison between different bagging variants.

We study the problem of estimating the distribution of the out-of-sample prediction error associated with ridge regression. In contrast, the traditional object of study is the uncentered second moment of this distribution (the mean squared prediction error), which can be estimated using cross-validation methods. We show that both generalized and leave-one-out cross-validation (GCV and LOOCV) for ridge regression can be suitably extended to estimate the full error distribution. This is still possible in a high-dimensional setting where the ridge regularization parameter is zero. In an asymptotic framework in which the feature dimension and sample size grow proportionally, we prove that almost surely, with respect to the training data, our estimators (extensions of GCV and LOOCV) converge weakly to the true out-of-sample error distribution. This result requires mild assumptions on the response and feature distributions. We also establish a more general result that allows us to estimate certain functionals of the error distribution, both linear and nonlinear. This yields various applications, including consistent estimation of the quantiles of the out-of-sample error distribution, which gives rise to prediction intervals with asymptotically exact coverage conditional on the training data.

With the ever-growing demand of Electric Vehicles (EV), the demand of the EV charging stations (EVCS) and energy is also increasing. The reason for switching to EV is to reduce CO2 emission, put a check on pollution and open doors for sustainable development. While most of the EV Charging stations are sourcing energy from Grids (i.e. coal burning) they cannot be considered Environment friendly. Use of Solar panel & Wind turbine produced energy comes with its own challenges like availability of land & Transmission of electricity. Thus, the paper aims to rectify the energy crisis by suggesting an alternate clean energy system i.e. Floating Solar photovoltaic (FSPV) to power Electric Vehicles (EV) considering various location challenges and transmission challenges. A neoteric hybrid model is suggested by making use of SAR, spatial (GIS) data, potential of Floating PV cells, to setup new locations of EV charging stations sourcing clean electricity from FSPVs or for transmission of the energy to existing EVCS.

We examine generalized and leave-one-out cross-validation for ridge regression in a proportional asymptotic framework where the dimension of the feature space grows proportionally with the number of observations. Given i.i.d. samples from a linear model with an arbitrary feature covariance and a signal vector that is bounded in $\ell_2$ norm, we show that generalized cross-validation for ridge regression converges almost surely to the expected out-of-sample prediction error, uniformly over a range of ridge regularization parameters that includes zero (and even negative values). We prove the analogous result for leave-one-out cross-validation. As a consequence, we show that ridge tuning via minimization of generalized or leave-one-out cross-validation asymptotically almost surely delivers the optimal level of regularization for predictive accuracy, whether it be positive, negative, or zero.

Uplink-downlink duality refers to the fact that under a sum-power constraint, the capacity regions of a Gaussian multiple-access channel and a Gaussian broadcast channel with Hermitian transposed channel matrices are identical. This paper generalizes this result to a cooperative cellular network, in which remote access-points are deployed as relays in serving the users under the coordination of a central processor (CP). In this model, the users and the relays are connected over noisy wireless links, while the relays and the CP are connected over noiseless but rate-limited fronthaul links. Based on a Lagrangian technique, this paper establishes a duality relationship between such a multiple-access relay channel and broadcast relay channel, under the assumption that the relays use compression-based strategies. Specifically, we show that under the same total transmit power constraint and individual fronthaul rate constraints, the achievable rate regions of the Gaussian multiple-access and broadcast relay channels are identical, when either independent compression or Wyner-Ziv and multivariate compression strategies are used. The key observations are that if the beamforming vectors at the relays are fixed, the sum-power minimization problems under the achievable rate and fronthaul constraints in both the uplink and the downlink can be transformed into either a linear programming or a semidefinite programming problem depending on the compression technique, and that the uplink and downlink problems are Lagrangian duals of each other. Moreover, the dual variables corresponding to the downlink rate constraints become the uplink powers; the dual variables corresponding to the downlink fronthaul constraints become the uplink quantization noises. This duality relationship enables an efficient algorithm for optimizing the downlink transmission and relaying strategies based on the uplink.

This paper studies the downlink of a cloud radio access network (C-RAN) in which a centralized processor (CP) communicates with mobile users through base stations (BSs) that are connected to the CP via finite-capacity fronthaul links. Information theoretically, the downlink of a C-RAN is modeled as a two-hop broadcast-relay network. Among the various transmission and relaying strategies for such model, this paper focuses on the compression strategy, in which the CP centrally encodes the signals to be broadcast jointly by the BSs, then compresses and sends these signals to the BSs through the fronthaul links. We characterize an achievable rate region for a generalized compression strategy with Marton's multicoding for broadcasting and multivariate compression for fronthaul transmission. We then compare this rate region with the distributed decode-forward (DDF) scheme, which achieves the capacity of the general relay networks to within a constant gap, and show that the difference lies in that DDF performs Marton's multicoding and multivariate compression jointly as opposed to successively as in the compression strategy. A main result of this paper is that under the assumption that the fronthaul links are subject to a sum capacity constraint, this difference is immaterial; so, for the Gaussian network, the compression strategy based on successive encoding can already achieve the capacity region of the C-RAN to within a constant gap, where the gap is independent of the channel parameters and the power constraints at the BSs. As a further result, for C-RAN under individual fronthaul constraints, this paper also establishes that the compression strategy can achieve to within a constant gap to the sum capacity.

This paper studies transmission strategies for the downlink of a cloud radio access network, in which the base stations are connected to a centralized cloud computing-based processor with digital fronthaul or backhaul links. We provide a system-level performance comparison of two fundamentally different strategies, namely, the data-sharing strategy and the compression strategy, which differ in the way the fronthaul/backhaul is utilized. It is observed that the performance of both strategies depends crucially on the available fronthaul or backhaul capacity. When the fronthaul/backhaul capacity is low, the data-sharing strategy performs better, while under moderate-to-high fronthaul/backhaul capacity, the compression strategy is superior. Using insights from such a comparison, we propose a novel hybrid strategy, combining the data-sharing and compression strategies, which allows for better control over the fronthaul/backhaul capacity utilization. An optimization framework for the hybrid strategy is proposed. Numerical evidence demonstrates the performance gain of the hybrid strategy.

We study error correction codes for multimedia streaming applications where a stream of source packets must be transmitted in real-time, with in-order decoding, and strict delay constraints. In our setup, the encoder observes a stream of source packets in a sequential fashion, and M channel packets must be transmitted between the arrival of successive source packets. Each channel packet can depend on all the source packets observed up to and including that time, but not on any future source packets. The decoder must reconstruct the source stream with a delay of T packets. We consider a class of packet erasure channels with burst and isolated erasures, where the erasure patterns are locally constrained. Our proposed model provides a tractable approximation to statistical models, such as the Gilbert-Elliott channel, for capacity analysis. When M = 1, i.e., when the source-packet arrival and channel-packet transmission rates are equal, we establish upper and lower bounds on the capacity, that are within one unit of the decoding delay T. We also establish necessary and sufficient conditions on the column distance and column span of a convolutional code to be feasible, and in turn establish a fundamental tradeoff between these. Our proposed codes-maximum distance and span codes- achieve a near-optimal tradeoff between the column distance and column span, and involve a layered construction. When M > 1, we establish the capacity for the burst-erasure channel and an achievable rate in the general case. Extensive numerical simulations over Gilbert-Elliott and Fritchman channel models suggest that our codes also achieve significant gains in the residual loss probability over statistical channel models.

Uplink-downlink duality refers to the fact that the Gaussian broadcast channel has the same capacity region as the dual Gaussian multiple-access channel under the same sum-power constraint. This paper investigates a similar duality relationship between the uplink and downlink of a cloud radio access network (C-RAN), where a central processor (CP) cooperatively serves multiple mobile users through multiple remote radio heads (RRHs) connected to the CP with finite-capacity fronthaul links. The uplink of such a C-RAN model corresponds to a multiple-access relay channel; the downlink corresponds to a broadcast relay channel. This paper considers compression-based relay strategies in both uplink and downlink C-RAN, where the quantization noise levels are functions of the fronthaul link capacities. If the fronthaul capacities are infinite, the conventional uplink-downlink duality applies. The main result of this paper is that even when the fronthaul capacities are finite, duality continues to hold for the case where independent compression is applied across each RRH in the sense that when the transmission and compression designs are jointly optimized, the achievable rate regions of the uplink and downlink remain identical under the same sum-power and individual fronthaul capacity constraints. As an application of the duality result, the power minimization problem in downlink C-RAN can be efficiently solved based on its uplink counterpart.