arXiv subjects

Mikael Skoglund

Publications and source records attributed to Mikael Skoglund.

At least 145 records · Page 8Linked to original sources

arXiv2021

Upper Bounds on the Generalization Error of Private Algorithms for Discrete Data

In this work, we study the generalization capability of algorithms from an information-theoretic perspective. It has been shown that the expected generalization error of an algorithm is bounded from above by a function of the relative entropy between the conditional probability distribution of the algorithm's output hypothesis, given the dataset with which it was trained, and its marginal probability distribution. We build upon this fact and introduce a mathematical formulation to obtain upper bounds on this relative entropy. Assuming that the data is discrete, we then develop a strategy using this formulation, based on the method of types and typicality, to find explicit upper bounds on the generalization error of stable algorithms, i.e., algorithms that produce similar output hypotheses given similar input datasets. In particular, we show the bounds obtained with this strategy for the case of $ε$-DP and $μ$-GDP algorithms.

cs.IT↗

arXiv2021

A Variational Approach to Privacy and Fairness

In this article, we propose a new variational approach to learn private and/or fair representations. This approach is based on the Lagrangians of a new formulation of the privacy and fairness optimization problems that we propose. In this formulation, we aim to generate representations of the data that keep a prescribed level of the relevant information that is not shared by the private or sensitive data, while minimizing the remaining information they keep. The proposed approach (i) exhibits the similarities of the privacy and fairness problems, (ii) allows us to control the trade-off between utility and privacy or fairness through the Lagrange multiplier parameter, and (iii) can be comfortably incorporated to common representation learning algorithms such as the VAE, the $β$-VAE, the VIB, or the nonlinear IB.

stat.ML↗

arXiv2021

Secure Block Source Coding with Sequential Encoding

We introduce fundamental bounds on achievable cumulative rate distribution functions (CRDF) to characterize a sequential encoding process that ensures lossless or lossy reconstruction subject to an average distortion criterion using a non-causal decoder. The CRDF describes the rate resources spent sequentially to compress the sequence. We also include a security constraint that affects the set of achievable CRDF. The information leakage is defined sequentially based on the mutual information between the source and its compressed representation, as it evolves. To characterize the security constraints, we introduce the concept of cumulative leakage distribution functions (CLF), which determines the allowed information leakage as distributed over encoded sub-blocks. Utilizing tools from majorization theory, we derive necessary and sufficient conditions on the achievable CRDF for a given independent and identically distributed (IID) source and CLF. One primary result of this paper is that the concave-hull of the CRDF characterizes the optimal achievable rate distribution.

cs.IT↗

arXiv2021

Testing for directed information graphs

In this paper, we study a hypothesis test to determine the underlying directed graph structure of nodes in a network, where the nodes represent random processes and the direction of the links indicate a causal relationship between said processes. Specifically, a k-th order Markov structure is considered for them, and the chosen metric to determine a connection between nodes is the directed information. The hypothesis test is based on the empirically calculated transition probabilities which are used to estimate the directed information. For a single edge, it is proven that the detection probability can be chosen arbitrarily close to one, while the false alarm probability remains negligible. When the test is performed on the whole graph, we derive bounds for the false alarm and detection probabilities, which show that the test is asymptotically optimal by properly setting the threshold test and using a large number of samples. Furthermore, we study how the convergence of the measures relies on the existence of links in the true graph.

cs.IT↗

arXiv2021

Data Disclosure with Non-zero Leakage and Non-invertible Leakage Matrix

We study a statistical signal processing privacy problem, where an agent observes useful data $Y$ and wants to reveal the information to a user. Since the useful data is correlated with the private data $X$, the agent employs a privacy mechanism to generate data $U$ that can be released. We study the privacy mechanism design that maximizes the revealed information about $Y$ while satisfying a strong $\ell_1$-privacy criterion. When a sufficiently small leakage is allowed, we show that the optimizer vectors of the privacy mechanism design problem have a specific geometry, i.e., they are perturbations of fixed vector distributions. This geometrical structure allows us to use a local approximation of the conditional entropy. By using this approximation the original optimization problem can be reduced to a linear program so that an approximate solution for privacy mechanism can be easily obtained. The main contribution of this work is to consider non-zero leakage with a non-invertible leakage matrix. In an example inspired by water mark application, we first investigate the accuracy of the approximation. Then, we employ different measures for utility and privacy leakage to compare the privacy-utility trade-off using our approach with other methods. In particular, it has been shown that by allowing small leakage, significant utility can be achieved using our method compared to the case where no leakage is allowed.

cs.IT↗

arXiv2021

Adaptive Stochastic ADMM for Decentralized Reinforcement Learning in Edge Industrial IoT

Edge computing provides a promising paradigm to support the implementation of Industrial Internet of Things (IIoT) by offloading tasks to nearby edge nodes. Meanwhile, the increasing network size makes it impractical for centralized data processing due to limited bandwidth, and consequently a decentralized learning scheme is preferable. Reinforcement learning (RL) has been widely investigated and shown to be a promising solution for decision-making and optimal control processes. For RL in a decentralized setup, edge nodes (agents) connected through a communication network aim to work collaboratively to find a policy to optimize the global reward as the sum of local rewards. However, communication costs, scalability and adaptation in complex environments with heterogeneous agents may significantly limit the performance of decentralized RL. Alternating direction method of multipliers (ADMM) has a structure that allows for decentralized implementation, and has shown faster convergence than gradient descent based methods. Therefore, we propose an adaptive stochastic incremental ADMM (asI-ADMM) algorithm and apply the asI-ADMM to decentralized RL with edge-computing-empowered IIoT networks. We provide convergence properties for proposed algorithms by designing a Lyapunov function and prove that the asI-ADMM has $O(\frac{1}{k}) +O(\frac{1}{M})$ convergence rate where $k$ and $ M$ are the number of iterations and batch samples, respectively. Then, we test our algorithm with two supervised learning problems. For performance evaluation, we simulate two applications in decentralized RL settings with homogeneous and heterogeneous agents. The experiment results show that our proposed algorithms outperform the state of the art in terms of communication costs and scalability, and can well adapt to complex IoT environments.

cs.LG↗

arXiv2021

Adaptive Interference Coordination over Channels with Unknown State at the Encoder and the Decoder

We generalize the problem of controlling the interference created to an external observer while communicating over a discrete memoryless channel (DMC) which was studied in \cite{serrano:2014}. In particular, we consider the scenario where the transmission is established over a compound DMC channel with unknown state at both the encoder and the decoder. Depending on the exact state $s$ of the channel, we ask for a different level of average precision $Δ_s$ on the establishment of the interference coordination with the external observer. For this set-up, we fully characterize the capacity region.

cs.IT↗

arXiv2021

A Model Randomization Approach to Statistical Parameter Privacy

In this paper, we study a privacy filter design problem for a sequence of sensor measurements whose joint probability density function (p.d.f.) depends on a private parameter. To ensure parameter privacy, we propose a filter design framework which consists of two components: a randomizer and a nonlinear transformation. The randomizer takes the private parameter as input and randomly generates a pseudo parameter. The nonlinear mapping transforms the measurements such that the joint p.d.f. of the filter's output depends on the pseudo parameter rather than the private parameter. It also ensures that the joint p.d.f. of the filter's output belongs to the same family of distributions as that of the measurements. The nonlinear transformation has a feedforward-feedback structure that allows real-time and causal generation of the disguised measurements with low complexity using a recursive structure. The design of the randomizer is formulated as an optimization problem subject to a privacy constraint, in terms of mutual information, and it is shown that the optimal randomizer is the solution of a convex optimization problem. Using information-theoretic inequalities, we show that the performance of any estimator of the private parameter, based on the output of the privacy filter, is limited by the privacy constraint. The structure of the nonlinear transformation is studied in the special cases of independent and identically distributed, Markovian, and Gauss-Markov measurements. Our results show that the privacy filter in the Gauss-Markov case can be implemented as two one-step ahead Kalman predictors and a set of minimum mean square error predictors. The Kalman predictors significantly reduce the complexity of computing the disguised measurements. A numerical example on occupancy privacy in a building automation system illustrates the approach.

eess.SY↗

arXiv2021

$(ε, n)$ Fixed-Length Strong Coordination Capacity

This paper investigates the problem of synthesizing joint distributions in the finite-length regime. For a fixed blocklength $n$ and an upper bound on the distribution approximation $ε$, we prove a capacity result for fixed-length strong coordination. It is shown analytically that the rate conditions for the fixed-length regime are lower-bounded by the mutual information that appears in the asymptotical condition plus $Q^{-1} \left(ε\right) \sqrt{ V/n}$, where $V$ is the channel dispersion, and $Q^{-1}$ is the inverse of the Gaussian cumulative distribution function.

cs.IT↗

arXiv2021

Generic Variance Bounds on Estimation and Prediction Errors in Time Series Analysis: An Entropy Perspective

In this paper, we obtain generic bounds on the variances of estimation and prediction errors in time series analysis via an information-theoretic approach. It is seen in general that the error bounds are determined by the conditional entropy of the data point to be estimated or predicted given the side information or past observations. Additionally, we discover that in order to achieve the prediction error bounds asymptotically, the necessary and sufficient condition is that the "innovation" is asymptotically white Gaussian. When restricted to Gaussian processes and 1-step prediction, our bounds are shown to reduce to the Kolmogorov-Szegö formula and Wiener-Masani formula known from linear prediction theory.

cs.IT↗

arXiv2021

Optimal Maximal Leakage-Distortion Tradeoff

Most methods for publishing data with privacy guarantees introduce randomness into datasets which reduces the utility of the published data. In this paper, we study the privacy-utility tradeoff by taking maximal leakage as the privacy measure and the expected Hamming distortion as the utility measure. We study three different but related problems. First, we assume that the data-generating distribution (i.e., the prior) is known, and we find the optimal privacy mechanism that achieves the smallest distortion subject to a constraint on maximal leakage. Then, we assume that the prior belongs to some set of distributions, and we formulate a min-max problem for finding the smallest distortion achievable for the worst-case prior in the set, subject to a maximal leakage constraint. Lastly, we define a partial order on privacy mechanisms based on the largest distortion they generate. Our results show that when the prior distribution is known, the optimal privacy mechanism fully discloses symbols with the largest prior probabilities, and suppresses symbols with the smallest prior probabilities. Furthermore, we show that sets of priors that contain more uniform distributions lead to larger distortion, while privacy mechanisms that distribute the privacy budget more uniformly over the symbols create smaller worst-case distortion.

cs.IT↗

arXiv2021

Quantifying Membership Privacy via Information Leakage

Machine learning models are known to memorize the unique properties of individual data points in a training set. This memorization capability can be exploited by several types of attacks to infer information about the training data, most notably, membership inference attacks. In this paper, we propose an approach based on information leakage for guaranteeing membership privacy. Specifically, we propose to use a conditional form of the notion of maximal leakage to quantify the information leaking about individual data entries in a dataset, i.e., the entrywise information leakage. We apply our privacy analysis to the Private Aggregation of Teacher Ensembles (PATE) framework for privacy-preserving classification of sensitive data and prove that the entrywise information leakage of its aggregation mechanism is Schur-concave when the injected noise has a log-concave probability density. The Schur-concavity of this leakage implies that increased consensus among teachers in labeling a query reduces its associated privacy cost. Finally, we derive upper bounds on the entrywise information leakage when the aggregation mechanism uses Laplace distributed noise.

cs.IT↗

arXiv2021

A Design Framework for Strongly $χ^2$-Private Data Disclosure

In this paper, we study a stochastic disclosure control problem using information-theoretic methods. The useful data to be disclosed depend on private data that should be protected. Thus, we design a privacy mechanism to produce new data which maximizes the disclosed information about the useful data under a strong $χ^2$-privacy criterion. For sufficiently small leakage, the privacy mechanism design problem can be geometrically studied in the space of probability distributions by a local approximation of the mutual information. By using methods from Euclidean information geometry, the original highly challenging optimization problem can be reduced to a problem of finding the principal right-singular vector of a matrix, which characterizes the optimal privacy mechanism. In two extensions we first consider a scenario where an adversary receives a noisy version of the user's message and then we look for a mechanism which finds $U$ based on observing $X$, maximizing the mutual information between $U$ and $Y$ while satisfying the privacy criterion on $U$ and $Z$ under the Markov chain $(Z,Y)-X-U$.

cs.IT↗

arXiv2021

A Learning-Based Approach to Address Complexity-Reliability Tradeoff in OS Decoders

In this paper, we study the tradeoffs between complexity and reliability for decoding large linear block codes. We show that using artificial neural networks to predict the required order of an ordered statistics based decoder helps in reducing the average complexity and hence the latency of the decoder. We numerically validate the approach through Monte Carlo simulations.

cs.IT↗

arXiv2021

Quadratic Signaling Games with Channel Combining Ratio

In this study, Nash and Stackelberg equilibria of single-stage and multi-stage quadratic signaling games between an encoder and a decoder are investigated. In the considered setup, the objective functions of the encoder and the decoder are misaligned, there is a noisy channel between the encoder and the decoder, the encoder has a soft power constraint, and the decoder has also noisy observation of the source to be estimated. We show that there exist only linear encoding and decoding strategies at the Stackelberg equilibrium, and derive the equilibrium strategies and costs. Regarding the Nash equilibrium, we explicitly characterize affine equilibria for the single-stage setup and show that the optimal encoder (resp. decoder) is affine for an affine decoder (resp. encoder) for the multi-stage setup. For the decoder side, between the information coming from the encoder and noisy observation of the source, our results describe what should be the combining ratio of these two channels. Regarding the encoder, we derive the conditions under which it is meaningful to transmit a message.

math.OC↗

arXiv2021

On Random Subset Generalization Error Bounds and the Stochastic Gradient Langevin Dynamics Algorithm

In this work, we unify several expected generalization error bounds based on random subsets using the framework developed by Hellström and Durisi [1]. First, we recover the bounds based on the individual sample mutual information from Bu et al. [2] and on a random subset of the dataset from Negrea et al. [3]. Then, we introduce their new, analogous bounds in the randomized subsample setting from Steinke and Zakynthinou [4], and we identify some limitations of the framework. Finally, we extend the bounds from Haghifam et al. [5] for Langevin dynamics to stochastic gradient Langevin dynamics and we refine them for loss functions with potentially large gradient norms.

cs.IT↗

arXiv2021

Latency and Reliability Trade-off with Computational Complexity Constraints: OS Decoders and Generalizations

In this paper, we study the problem of latency and reliability trade-off in ultra-reliable low-latency communication (URLLC) in the presence of decoding complexity constraints. We consider linear block encoded codewords transmitted over a binary-input AWGN channel and decoded with order-statistic (OS) decoder. We first investigate the performance of OS decoders as a function of decoding complexity and propose an empirical model that accurately quantifies the corresponding trade-off. Next, a consistent way to compute the aggregate latency for complexity constrained receivers is presented, where the latency due to decoding is also included. It is shown that, with strict latency requirements, decoding latency cannot be neglected in complexity constrained receivers. Next, based on the proposed model, several optimization problems, relevant to the design of URLLC systems, are introduced and solved. It is shown that the decoding time has a drastic effect on the design of URLLC systems when constraints on decoding complexity are considered. Finally, it is also illustrated that the proposed model can closely describe the performance versus complexity trade-off for other candidate coding solutions for URLLC such as tail-biting convolutional codes, polar codes, and low-density parity-check codes.

cs.IT↗

arXiv2020

Neural Estimators for Conditional Mutual Information Using Nearest Neighbors Sampling

The estimation of mutual information (MI) or conditional mutual information (CMI) from a set of samples is a long-standing problem. A recent line of work in this area has leveraged the approximation power of artificial neural networks and has shown improvements over conventional methods. One important challenge in this new approach is the need to obtain, given the original dataset, a different set where the samples are distributed according to a specific product density function. This is particularly challenging when estimating CMI. In this paper, we introduce a new technique, based on k nearest neighbors (k-NN), to perform the resampling and derive high-confidence concentration bounds for the sample average. Then the technique is employed to train a neural network classifier and the CMI is estimated accordingly. We propose three estimators using this technique and prove their consistency, make a comparison between them and similar approaches in the literature, and experimentally show improvements in estimating the CMI in terms of accuracy and variance of the estimators.

cs.IT↗