arXiv subjects

Mohammad Hossein Yassaee

Publications and source records attributed to Mohammad Hossein Yassaee.

At least 19 recordsLinked to original sources

arXiv2026

Geometry-Adaptive Mechanisms for Private Synthetic Data

Generating differentially private synthetic data with meaningful Wasserstein utility guarantees is challenging in high dimensions. For datasets of size $n$ on $[0,1]^d$ with $d\ge2$, existing pure $\varepsilon$-differentially private mechanisms achieve expected $1$-Wasserstein error of order $(\varepsilon n)^{-1/d}$, reflecting the curse of dimensionality. While this rate is optimal in the worst case, it can be overly pessimistic when the data are supported on a lower-dimensional set. We formalize this through a multiscale packing-growth dimension $k$, which captures the geometric complexity of the support via the growth of packing numbers across scales. We propose \emph{Adaptive Pruned-PMM}, a pure $\varepsilon$-differentially private mechanism that combines private depth selection with our pruned variant of the Private Measure Mechanism (PMM) of He et al.\ (2023). The mechanism supports deeper, geometry-adapted hierarchies with expected running time $O\!\left(d(n+d)\log(\varepsilon n)\right)$, which is near-linear in $n$ for fixed dimension and privacy budget. Under an external multiscale packing-growth condition with dimension $k$, we show that, for fixed positive privacy budgets and fixed geometry, the expected $1$-Wasserstein error is of order $(\varepsilon n)^{-1/k}$ for $k>1$ as $n$ grows. We also prove a lower bound under a corresponding internal packing-growth condition, showing that the exponent $1/k$ is sharp within this framework.

cs.DS↗

arXiv2026

TRACE: Theoretical Risk Attribution under Covariate-shift Effects

When a source-trained model $Q$ is replaced by a model $\tilde{Q}$ trained on shifted data, its performance on the source domain can change unpredictably. To address this, we study the two-model risk change, $ΔR := R_P(\tilde{Q}) - R_P(Q)$, under covariate shift. We introduce TRACE (Theoretical Risk Attribution under Covariate-shift Effects), a framework that decomposes $|ΔR|$ into an interpretable upper bound. This decomposition disentangles the risk change into four actionable factors: two generalization gaps, a model change penalty, and a covariate shift penalty, transforming the bound into a powerful diagnostic tool for understanding why performance has changed. To make TRACE a fully computable diagnostic, we instantiate each term. The covariate shift penalty is estimated via a model sensitivity factor (from high-quantile input gradients) and a data-shift measure; we use feature-space Optimal Transport (OT) by default and provide a robust alternative using Maximum Mean Discrepancy (MMD). The model change penalty is controlled by the average output distance between the two models on the target sample. Generalization gaps are estimated on held-out data. We validate our framework in an idealized linear regression setting, showing the TRACE bound correctly captures the scaling of the true risk difference with the magnitude of the shift. Across synthetic and vision benchmarks, TRACE diagnostics are valid and maintain a strong monotonic relationship with the true performance degradation. Crucially, we derive a deployment gate score that correlates strongly with $|ΔR|$ and achieves high AUROC/AUPRC for gating decisions, enabling safe, label-efficient model replacement.

cs.LG↗

arXiv2026

A Class of Subadditive Information Measures and their Applications

We introduce a two-parameter family of discrepancy measures, termed \emph{$(G,f)$-divergences}, obtained by applying a non-decreasing function $G$ to an $f$-divergence $D_f$. Building on Csiszár's formulation of mutual $f$-information, we define a corresponding $(G,f)$-information measure $ I_{G,f}(X;Y)$. A central theme of the paper is subadditivity over product distributions and product channels. We develop reduction principles showing that, for broad classes of $G$, it suffices to verify divergence subadditivity on binary alphabets. Specializing to the functions $G(x)\in\{x,\log(1+x),-\log(1-x)\}$, we derive tractable sufficient conditions on $f$ that guarantee subadditivity, covering many standard $f$-divergences. Finally, we present applications to finite-blocklength converses for channel coding, bounds in binary hypothesis testing, and an extension of the Shannon--Gallager--Berlekamp sphere-packing exponent framework to subadditive $(G,f)$-divergences.

cs.IT↗

arXiv2025

Fundamental limits of distributed covariance matrix estimation via a conditional strong data processing inequality

Estimating high-dimensional covariance matrices is a key task across many fields. This paper explores the theoretical limits of distributed covariance estimation in a feature-split setting, where communication between agents is constrained. Specifically, we study a scenario in which multiple agents each observe different components of i.i.d. samples drawn from a sub-Gaussian random vector. A central server seeks to estimate the complete covariance matrix using a limited number of bits communicated by each agent. We obtain a nearly tight minimax lower bound for covariance matrix estimation under operator norm and Frobenius norm. Our main technical tool is a novel generalization of the strong data processing inequality (SDPI), termed the Conditional Strong Data Processing Inequality (C-SDPI) coefficient, introduced in this work. The C-SDPI coefficient shares key properties such as tensorization with the conventional SDPI. Crucially, it quantifies the average contraction in a state-dependent channel and can be significantly lower than the worst-case SDPI coefficient over the state input. Utilizing the doubling trick of Geng-Nair and an operator Jensen inequality, we compute this coefficient for Gaussian mixture channels. We then employ it to establish minimax lower bounds on estimation error, capturing the trade-offs among sample size, communication cost, and data dimensionality. Building on this, we present a nearly optimal estimation protocol whose sample and communication requirements match the lower bounds up to logarithmic factors. Unlike much of the existing literature, our framework does not assume infinite samples or Gaussian distributions, making it broadly applicable. Finally, we extend our analysis to interactive protocols, showing interaction can significantly reduce communication requirements compared to non-interactive schemes.

stat.ML↗

arXiv2025

A New Approach to Backtracking Counterfactual Explanations: A Unified Causal Framework for Efficient Model Interpretability

Counterfactual explanations enhance interpretability by identifying alternative inputs that produce different outputs, offering localized insights into model decisions. However, traditional methods often neglect causal relationships, leading to unrealistic examples. While newer approaches integrate causality, they are computationally expensive. To address these challenges, we propose an efficient method called BRACE based on backtracking counterfactuals that incorporates causal reasoning to generate actionable explanations. We first examine the limitations of existing methods and then introduce our novel approach and its features. We also explore the relationship between our method and previous techniques, demonstrating that it generalizes them in specific scenarios. Finally, experiments show that our method provides deeper insights into model outputs.

cs.LG↗

arXiv2024

Output Statistics of Random Binning: Tsallis Divergence and Its Applications

Random binning is a widely used technique in information theory with diverse applications. In this paper, we focus on the output statistics of random binning (OSRB) using the Tsallis divergence $T_α$. We analyze all values of $α\in (0, \infty)\cup\{\infty\}$ and consider three scenarios: (i) the binned sequence is generated i.i.d., (ii) the sequence is randomly chosen from an $ε$-typical set, and (iii) the sequence originates from an $ε$-typical set and is passed through a non-memoryless virtual channel. Our proofs cover both achievability and converse results. To address the unbounded nature of $T_\infty$, we extend the OSRB framework using Rényi's divergence with order infinity, denoted $D_\infty$. As part of our exploration, we analyze a specific form of Rényi's conditional entropy and its properties. Additionally, we demonstrate the application of this framework in deriving achievability results for the wiretap channel, where Tsallis divergence serves as a security measure. The secure rate we obtain through the OSRB analysis matches the secure capacity for $α\in (0, 2]\cup\{{\infty}\}$ and serves as a potential candidate for the secure capacity when $α\in (2, \infty)$.

cs.IT↗

arXiv2023

f-divergences and their applications in lossy compression and bounding generalization error

In this paper, we provide three applications for $f$-divergences: (i) we introduce Sanov's upper bound on the tail probability of the sum of independent random variables based on super-modular $f$-divergence and show that our generalized Sanov's bound strictly improves over ordinary one, (ii) we consider the lossy compression problem which studies the set of achievable rates for a given distortion and code length. We extend the rate-distortion function using mutual $f$-information and provide new and strictly better bounds on achievable rates in the finite blocklength regime using super-modular $f$-divergences, and (iii) we provide a connection between the generalization error of algorithms with bounded input/output mutual $f$-information and a generalized rate-distortion problem. This connection allows us to bound the generalization error of learning algorithms using lower bounds on the $f$-rate-distortion function. Our bound is based on a new lower bound on the rate-distortion function that (for some examples) strictly improves over previously best-known bounds.

cs.IT↗

arXiv2022

Learning under Distribution Mismatch and Model Misspecification

We study learning algorithms when there is a mismatch between the distributions of the training and test datasets of a learning algorithm. The effect of this mismatch on the generalization error and model misspecification are quantified. Moreover, we provide a connection between the generalization error and the rate-distortion theory, which allows one to utilize bounds from the rate-distortion theory to derive new bounds on the generalization error and vice versa. In particular, the rate-distortion based bound strictly improves over the earlier bound by Xu and Raginsky even when there is no mismatch. We also discuss how "auxiliary loss functions" can be utilized to obtain upper bounds on the generalization error.

cs.IT↗

arXiv2021

Sequential Estimation under Multiple Resources: a Bandit Point of View

The problem of Sequential Estimation under Multiple Resources (SEMR) is defined in a federated setting. SEMR could be considered as the intersection of statistical estimation and bandit theory. In this problem, an agent is confronting with k resources to estimate a parameter $θ$. The agent should continuously learn the quality of the resources by wisely choosing them and at the end, proposes an estimator based on the collected data. In this paper, we assume that the resources' distributions are Gaussian. The quality of the final estimator is evaluated by its mean squared error. Also, we restrict our class of estimators to unbiased estimators in order to define a meaningful notion of regret. The regret measures the performance of the agent by the variance of the final estimator in comparison to the optimal variance. We propose a lower bound to determine the fundamental limit of the setting even in the case that the distributions are not Gaussian. Also, we offer an order-optimal algorithm to achieve this lower bound.

cs.LG↗

arXiv2020

State Masking Over a Two-State Compound Channel

We consider fundamental limits for communicating over a compound channel when the state of the channel needs to be masked. Our model is closely related to an area of study known as covert communication that is a setting in which the transmitter wishes to communicate to legitimate receiver(s) while ensuring that the communication is not detected by an adversary. The main contribution in our two-state masking setup is the establishment of bounds on the throughput-key region when the constraint that quantifies how much the states are masked is defined to be the total variation distance between the two channel-induced distributions. For the scenario in which the key length is infinite, we provide sufficient conditions for when the bounds to coincide for the throughput, which follows the square-root law. Numerical examples, including that of a Gaussian channel, are provided to illustrate our results.

cs.IT↗

arXiv2019

Covert Communication Over a Compound Channel

In this paper, we consider fundamental communication limits over a compound channel. Covert communication in the information-theoretic context has been primarily concerned with fundamental limits when the transmitter wishes to communicate to legitimate receiver(s) while ensuring that the communication is not detected by an adversary. This paper, however, considers an alternative, and no less important, setting in which the object to be masked is the state of the compound channel. Such a communication model has applications in the prevention of malicious parties seeking to jam the communication signal when, for example, the signal-to-noise ratio of a wireless channel is found to be low. Our main contribution is the establishment of bounds on the throughput-key region when the covertness constraint is defined in terms of the total variation distance. In addition, for the scenario in which the key length is infinite, we provide a sufficient condition for when the bounds coincide for the scaling of the throughput, which follows the square-root law. Numerical examples, including that of a Gaussian channel, are provided to illustrate our results.

cs.IT↗

arXiv2019

Almost exact analysis of soft covering lemma via large deviation

This paper investigates the soft covering lemma under both the relative entropy and the total variation distance as the measures of deviation. The exact order of the expected deviation of the random i.i.d. code for the soft covering problem problem, is determined. The proof technique used in this paper significantly differs from the previous techniques for deriving exact exponent of the soft covering lemma. The achievability of the exact order follows from applying the change of measure trick (which has been broadly used in the large deviation) to the known one-shot bounds in the literature. For the ensemble converse, some new inequalities of independent interest derived and then the change of measure trick is applied again. The exact order of the total variation distance is similar to the exact order of the error probability, thus it adds another duality between the channel coding and soft covering. Finally, The results of this paper are valid for any memoryless channels, not only channels with finite alphabets.

cs.IT↗

arXiv2018

A Correlation Measure Based on Vector-Valued $L_p$-Norms

In this paper, we introduce a new measure of correlation for bipartite quantum states. This measure depends on a parameter $α$, and is defined in terms of vector-valued $L_p$-norms. The measure is within a constant of the exponential of $α$-Rényi mutual information, and reduces to the trace norm (total variation distance) for $α=1$. We will prove some decoupling type theorems in terms of this measure of correlation, and present some applications in privacy amplification as well as in bounding the random coding exponents. In particular, we establish a bound on the secrecy exponent of the wiretap channel (under the total variation metric) in terms of the $α$-Rényi mutual information according to \emph{Csiszár's proposal}.

cs.IT↗

arXiv2016

Simulation of a Channel with Another Channel

In this paper, we study the problem of simulating a DMC channel from another DMC channel under an average-case and an exact model. We present several achievability and infeasibility results, with tight characterizations in special cases. In particular for the exact model, we fully characterize when a BSC channel can be simulated from a BEC channel when there is no shared randomness. We also provide infeasibility and achievability results for simulation of a binary channel from another binary channel in the case of no shared randomness. To do this, we use properties of Rényi capacity of a given order. We also introduce a notion of "channel diameter" which is shown to be additive and satisfy a data processing inequality.

cs.IT↗

arXiv2014

Achievability proof via output statistics of random binning

This paper introduces a new and ubiquitous framework for establishing achievability results in \emph{network information theory} (NIT) problems. The framework uses random binning arguments and is based on a duality between channel and source coding problems. {Further,} the framework uses pmf approximation arguments instead of counting and typicality. This allows for proving coordination and \emph{strong} secrecy problems where certain statistical conditions on the distribution of random variables need to be satisfied. These statistical conditions include independence between messages and eavesdropper's observations in secrecy problems and closeness to a certain distribution (usually, i.i.d. distribution) in coordination problems. One important feature of the framework is to enable one {to} add an eavesdropper and obtain a result on the secrecy rates "for free." We make a case for generality of the framework by studying examples in the variety of settings containing channel coding, lossy source coding, joint source-channel coding, coordination, strong secrecy, feedback and relaying. In particular, by investigating the framework for the lossy source coding problem over broadcast channel, it is shown that the new framework provides a simple alternative scheme to \emph{hybrid} coding scheme. Also, new results on secrecy rate region (under strong secrecy criterion) of wiretap broadcast channel and wiretap relay channel are derived. In a set of accompanied papers, we have shown the usefulness of the framework to establish achievability results for coordination problems including interactive channel simulation, coordination via relay and channel simulation via another channel.

cs.IT↗

arXiv2014

Channel simulation via interactive communications

In this paper, we study the problem of channel simulation via interactive communication, known as the coordination capacity, in a two-terminal network. We assume that two terminals observe i.i.d.\ copies of two random variables and would like to generate i.i.d.\ copies of two other random variables jointly distributed with the observed random variables. The terminals are provided with two-way communication links, and shared common randomness, all at limited rates. Two special cases of this problem are the interactive function computation studied by Ma and Ishwar, and the tradeoff curve between one-way communication and shared randomness studied by Cuff. The latter work had inspired Gohari and Anantharam to study the general problem of channel simulation via interactive communication stated above. However only inner and outer bounds for the special case of no shared randomness were obtained in their work. In this paper we settle this problem by providing an exact computable characterization of the multi-round problem. To show this we employ the technique of "output statistics of random binning" that has been recently developed by the authors.

cs.IT↗

arXiv2013

Non-Asymptotic Output Statistics of Random Binning and Its Applications

In this paper we develop a finite blocklength version of the Output Statistics of Random Binning (OSRB) framework. The framework is shown to be optimal in the point-to-point case. New second order regions for broadcast channel and wiretap channel with strong secrecy criterion are derived.

cs.IT↗

arXiv2013

A Technique for Deriving One-Shot Achievability Results in Network Information Theory

This paper proposes a novel technique to prove a one-shot version of achievability results in network information theory. The technique is not based on covering and packing lemmas. In this technique, we use an stochastic encoder and decoder with a particular structure for coding that resembles both the ML and the joint-typicality coders. Although stochastic encoders and decoders do not usually enhance the capacity region, their use simplifies the analysis. The Jensen inequality lies at the heart of error analysis, which enables us to deal with the expectation of many terms coming from stochastic encoders and decoders at once. The technique is illustrated via several examples: point-to-point channel coding, Gelfand-Pinsker, Broadcast channel (Marton), Berger-Tung, Heegard-Berger/Kaspi, Multiple description coding and Joint source-channel coding over a MAC. Most of our one-shot results are new. The asymptotic forms of these expressions is the same as that of classical results. Our one-shot bounds in conjunction with multi-dimensional Berry-Essen CLT imply new results in the finite blocklength regime. In particular applying the one-shot result for the memoryless broadcast channel in the asymptotic case, we get the entire region of Marton's inner bound without any need for time-sharing.

cs.IT↗