An $n$-dimensional source with memory is observed by $K$ isolated encoders via parallel channels, who compress their observations to transmit to the decoder via noiseless rate-constrained links while leveraging their memory of the past. At each time instant, the decoder receives $K$ new codewords from the observers, combines them with the past received codewords, and produces a minimum-distortion estimate of the latest block of $n$ source symbols. This scenario extends the classical one-shot CEO problem to multiple rounds of communication with communicators maintaining the memory of the past. We extend the Berger-Tung inner and outer bounds to the scenario with inter-block memory, showing that the minimum asymptotically (as $n \to \infty$) achievable sum rate required to achieve a target distortion is bounded by minimal directed mutual information problems. For the Gauss-Markov source observed via $K$ parallel AWGN channels, we show that the inner bound is tight and solve the corresponding minimal directed mutual information problem, thereby establishing the minimum asymptotically achievable sum rate. Finally, we explicitly bound the rate loss due to a lack of communication among the observers; that bound is attained with equality in the case of identical observation channels. The general coding theorem is proved via a new nonasymptotic bound that uses stochastic likelihood coders and whose asymptotic analysis yields an extension of the Berger-Tung inner bound to the causal setting. The analysis of the Gaussian case is facilitated by reversing the channels of the observers.
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This paper considers the problem of measure estimation under the barycentric coding model (BCM), in which an unknown measure is assumed to belong to the set of Wasserstein-2 barycenters of a finite set of known measures. Estimating a measure under this model is equivalent to estimating the unknown barycenteric coordinates. We provide novel geometrical, statistical, and computational insights for measure estimation under the BCM, consisting of three main results. Our first main result leverages the Riemannian geometry of Wasserstein-2 space to provide a procedure for recovering the barycentric coordinates as the solution to a quadratic optimization problem assuming access to the true reference measures. The essential geometric insight is that the parameters of this quadratic problem are determined by inner products between the optimal displacement maps from the given measure to the reference measures defining the BCM. Our second main result then establishes an algorithm for solving for the coordinates in the BCM when all the measures are observed empirically via i.i.d. samples. We prove precise rates of convergence for this algorithm -- determined by the smoothness of the underlying measures and their dimensionality -- thereby guaranteeing its statistical consistency. Finally, we demonstrate the utility of the BCM and associated estimation procedures in three application areas: (i) covariance estimation for Gaussian measures; (ii) image processing; and (iii) natural language processing.
The strong interference suffered by users can be a severe problem in cache-enabled networks (CENs) due to the content-centric user association mechanism. To tackle this issue, multi-antenna technology may be employed for interference management. In this paper, we consider a user-centric interference nulling (IN) scheme in two-tier multi-user multi-antenna CEN, with a hybrid most-popular and random caching policy at macro base stations (MBSs) and small base stations (SBSs) to provide file diversity. All the interfering SBSs within the IN range of a user are requested to suppress the interference at this user using zero-forcing beamforming. Using stochastic geometry analysis techniques, we derive a tractable expression for the area spectral efficiency (ASE). A lower bound on the ASE is also obtained, with which we then consider ASE maximization, by optimizing the caching policy and IN coefficient. To solve the resultant mixed integer programming problem, we design an alternating optimization algorithm to minimize the lower bound of the ASE. Our numerical results demonstrate that the proposed caching policy yields performance that is close to the optimum, and it outperforms several existing baselines.
This paper investigates the interference nulling capability of reconfigurable intelligent surface (RIS) in a multiuser environment where multiple single-antenna transceivers communicate simultaneously in a shared spectrum. From a theoretical perspective, we show that when the channels between the RIS and the transceivers have line-of-sight and the direct paths are blocked, it is possible to adjust the phases of the RIS elements to null out all the interference completely and to achieve the maximum $K$ degrees-of-freedom (DoF) in the overall $K$-user interference channel, provided that the number of RIS elements exceeds some finite value that depends on $K$. Algorithmically, for any fixed channel realization we formulate the interference nulling problem as a feasibility problem, and propose an alternating projection algorithm to efficiently solve the resulting nonconvex problem with local convergence guarantee. Numerical results show that the proposed alternating projection algorithm can null all the interference if the number of RIS elements is only slightly larger than a threshold of $2K(K-1)$. For the practical sum-rate maximization objective, this paper proposes to use the zero-forcing solution obtained from alternating projection as an initial point for subsequent Riemannian conjugate gradient optimization and shows that it has a significant performance advantage over random initializations. For the objective of maximizing the minimum rate, this paper proposes a subgradient projection method which is capable of achieving excellent performance at low complexity.
In this paper, we are interested in the performance of a variable-length stop-feedback (VLSF) code with $m$ optimal decoding times for the binary-input additive white Gaussian noise (BI-AWGN) channel. We first develop tight approximations on the tail probability of length-$n$ cumulative information density. Building on the work of Yavas \emph{et al.}, we formulate the problem of minimizing the upper bound on average blocklength subject to the error probability, minimum gap, and integer constraints. For this integer program, we show that for a given error constraint, a VLSF code that decodes after every symbol attains the maximum achievable rate. We also present a greedy algorithm that yields possibly suboptimal integer decoding times. By allowing a positive real-valued decoding time, we develop the gap-constrained sequential differential optimization (SDO) procedure. Numerical evaluation shows that the gap-constrained SDO can provide a good estimate on achievable rate of VLSF codes with $m$ optimal decoding times and that a finite $m$ suffices to attain Polyanskiy's bound for VLSF codes with $m = \infty$.
The capacity of finite state channels (FSCs) with feedback has been shown to be a limit of a sequence of multi-letter expressions. Despite many efforts, a closed-form single-letter capacity characterization is unknown to date. In this paper, the feedback capacity is studied from a fundamental algorithmic point of view by addressing the question of whether or not the capacity can be algorithmically computed. To this aim, the concept of Turing machines is used, which provides fundamental performance limits of digital computers. It is shown that the feedback capacity of FSCs is not Banach-Mazur computable and therefore not Turing computable. As a consequence, it is shown that either achievability or converse is not Banach-Mazur computable, which means that there are FSCs for which it is impossible to find computable tight upper and lower bounds. Furthermore, it is shown that the feedback capacity cannot be characterized as the maximization of a finite-letter formula of entropic quantities.
We consider finite-state channels (FSCs) where the channel state is stochastically dependent on the previous channel output. We refer to these as Noisy Output is the STate (NOST) channels. We derive the feedback capacity of NOST channels in two scenarios: with and without causal state information (CSI) available at the encoder. If CSI is unavailable, the feedback capacity is $C_{\text{FB}}= \max_{P(x|y')} I(X;Y|Y')$, while if it is available at the encoder, the feedback capacity is $C_{\text{FB-CSI}}= \max_{P(u|y'),x(u,s')} I(U;Y|Y')$, where $U$ is an auxiliary RV with finite cardinality. In both formulas, the output process is a Markov process with stationary distribution. The derived formulas generalize special known instances from the literature, such as where the state is i.i.d. and where it is a deterministic function of the output. $C_{\text{FB}}$ and $C_{\text{FB-CSI}}$ are also shown to be computable via convex optimization problem formulations. Finally, we present an example of an interesting NOST channel for which CSI available at the encoder does not increase the feedback capacity.
The Evidential regression network (ENet) estimates a continuous target and its predictive uncertainty without costly Bayesian model averaging. However, it is possible that the target is inaccurately predicted due to the gradient shrinkage problem of the original loss function of the ENet, the negative log marginal likelihood (NLL) loss. In this paper, the objective is to improve the prediction accuracy of the ENet while maintaining its efficient uncertainty estimation by resolving the gradient shrinkage problem. A multi-task learning (MTL) framework, referred to as MT-ENet, is proposed to accomplish this aim. In the MTL, we define the Lipschitz modified mean squared error (MSE) loss function as another loss and add it to the existing NLL loss. The Lipschitz modified MSE loss is designed to mitigate the gradient conflict with the NLL loss by dynamically adjusting its Lipschitz constant. By doing so, the Lipschitz MSE loss does not disturb the uncertainty estimation of the NLL loss. The MT-ENet enhances the predictive accuracy of the ENet without losing uncertainty estimation capability on the synthetic dataset and real-world benchmarks, including drug-target affinity (DTA) regression. Furthermore, the MT-ENet shows remarkable calibration and out-of-distribution detection capability on the DTA benchmarks.
We study the problem of learning in the stochastic shortest path (SSP) setting, where an agent seeks to minimize the expected cost accumulated before reaching a goal state. We design a novel model-based algorithm EB-SSP that carefully skews the empirical transitions and perturbs the empirical costs with an exploration bonus to guarantee both optimism and convergence of the associated value iteration scheme. We prove that EB-SSP achieves the minimax regret rate $\widetilde{O}(B_{\star} \sqrt{S A K})$, where $K$ is the number of episodes, $S$ is the number of states, $A$ is the number of actions and $B_{\star}$ bounds the expected cumulative cost of the optimal policy from any state, thus closing the gap with the lower bound. Interestingly, EB-SSP obtains this result while being parameter-free, i.e., it does not require any prior knowledge of $B_{\star}$, nor of $T_{\star}$ which bounds the expected time-to-goal of the optimal policy from any state. Furthermore, we illustrate various cases (e.g., positive costs, or general costs when an order-accurate estimate of $T_{\star}$ is available) where the regret only contains a logarithmic dependence on $T_{\star}$, thus yielding the first horizon-free regret bound beyond the finite-horizon MDP setting.
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.
M. Christandl conjectured that the composition of any trace preserving PPT map with itself is entanglement breaking. We prove that Christandl's conjecture holds asymptotically by showing that the distance between the iterates of any unital or trace preserving PPT map and the set of entanglement breaking maps tends to zero. Finally, for every graph we define a one-parameter family of maps on matrices and determine the least value of the parameter such that the map is variously, positive, completely positive, PPT and entanglement breaking in terms of properties of the graph. Our estimates are sharp enough to conclude that Christandl's conjecture holds for these families.
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