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1. A perspective on massive random-access

   Polyanskiy, Yury (June 2017, 2017 IEEE Int. Symp. Inf. Theory (ISIT))

   This paper discusses the contemporary problem of providing multiple-access (MAC) to a massive number of uncoordinated users. First, we define a random-access code for Ka-user Gaussian MAC to be a collection of norm-constrained vectors such that the noisy sum of any Ka of them can be decoded with a given (suitably defined) probability of error. An achievability bound for such codes is proposed and compared against popular practical solutions: ALOHA, coded slotted ALOHA, CDMA, and treating interference as noise. It is found out that as the number of users increases existing solutions become vastly energy-inefficient. Second, we discuss the asymptotic (in blocklength) problem of coding for a K-user Gaussian MAC when K is proportional to blocklength and each user’s payload is fixed. It is discovered that the energy-per-bit vs. spectral efficiency exhibits a rather curious tradeoff in this case. 

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2. Algebraic properties of solutions to common information of Gaussian vectors under sparse graphical constraints

   https://doi.org/10.1109/ALLERTON.2017.8262852  

   Moharrer, Ali; Wei, Shuangqing (October 2017, 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton))

   We formulate Wyner's common information for random vectors x ϵ R n with joint Gaussian density. We show that finding the common information of Gaussian vectors is equivalent to maximizing a log-determinant of the additive Gaussian noise covariance matrix. We coin such optimization problem as a constrained minimum determinant factor analysis (CMDFA) problem. The convexity of such problem with necessary and sufficient conditions on CMDFA solution is shown. We study the algebraic properties of CMDFA solution space, through which we study two sparse Gaussian graphical models, namely, latent Gaussian stars, and explicit Gaussian chains. Interestingly, we show that depending on pairwise covariance values in a Gaussian graphical structure, one may not always end up with the same parameters and structure for CMDFA solution as those found via graphical learning algorithms. In addition, our results suggest that Gaussian chains have little room left for dimension reduction in terms of the number of latent variables required in their CMDFA solutions. 

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3. Low complexity schemes for the random access Gaussian channel

   Ordentlich, Or; Polyanskiy, Yury (June 2017, 2017 IEEE Int. Symp. Inf. Theory (ISIT),)

   We consider an uncoordinated Gaussian multiple access channel with a relatively large number of active users within each block. A low complexity coding scheme is proposed, which is based on a combination of compute-and-forward and coding for a binary adder channel. For a wide regime of parameters of practical interest, the energy-per-bit required by each user in the proposed scheme is significantly smaller than that required by popular solutions such as slotted-ALOHA and treating interference as noise. 

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4. Sequential Estimation of Gaussian Process-Based Deep State-Space Models

   https://doi.org/10.1109/TSP.2023.3303648  

   Liu, Yuhao; Ajirak, Marzieh; Djurić, Petar M (January 2023, IEEE Transactions on Signal Processing)

   We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian processes that are implemented via random feature-based Gaussian processes. In these models, we have two sets of unknowns, highly nonlinear unknowns (the values of the latent processes) and conditionally linear unknowns (the constant parameters of the random feature-based Gaussian processes). We present a method based on particle filtering where the parameters of the random feature-based Gaussian processes are integrated out in obtaining the predictive density of the states and do not need particles. We also propose an ensemble version of the method, with each member of the ensemble having its own set of features. With several experiments, we show that the method can track the latent processes up to a scale and rotation. 

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5. Distributed nearest-neighbor Gaussian processes

   https://doi.org/10.1080/03610918.2021.1921798  

   Grenier, Isabelle; Sansó, Bruno (April 2021, Communications in Statistics - Simulation and Computation)

   null (Ed.)

   While many statistical approaches have tackled the problem of large spa- tial datasets, the issues arising from costly data movement and data stor- age have long been set aside. Having easy access to the data has been taken for granted and is now becoming an important bottleneck in the performance of statistical inference. As the availability of high resolution spatial data continues to grow, the need to develop efficient modeling techniques that leverage multi-processor and multi-storage capabilities is becoming a priority. To that end, the development of a distributed method to implement Nearest-Neighbor Gaussian Process (NNGP) models for spa- tial interpolation and inference for large datasets is of interest. The pro- posed framework retains the exact implementation of the NNGP while allowing for distributed or sequential computation of the posterior infer- ence. The method allows for any choice of grouping of the data whether it is at random or by region. As a result of this new method, the NNGP model can be implemented with an even split of the computation burden with minimum overload at the master node level. 

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