Related papers: Limits of the Kucera-Gacs coding method
Bayesian inference requires approximation methods to become computable, but for most of them it is impossible to quantify how close the approximation is to the true posterior. In this work, we present a theorem upper-bounding the KL…
This paper deals with the problem of universal lossless coding on a countable infinite alphabet. It focuses on some classes of sources defined by an envelope condition on the marginal distribution, namely exponentially decreasing envelope…
The classic model of computable randomness considers martingales that take real or rational values. Recent work by Bienvenu et al. (2012) and Teutsch (2014) shows that fundamental features of the classic model change when the martingales…
A fruitful way of obtaining meaningful, possibly concrete, algorithmically random numbers is to consider a potential behaviour of a Turing machine and its probability with respect to a measure (or semi-measure) on the input space of binary…
Bayesian optimization based on the Gaussian process upper confidence bound (GP-UCB) offers a theoretical guarantee for optimizing black-box functions. In practice, however, black-box functions often involve input uncertainty. To handle such…
The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…
We study randomness beyond $\Pi^1_1$-randomness and its Martin-L\"of type variant, introduced in \cite{MR2340241} and further studied in \cite{Continuous-higher-randomness}. The class given by the infinite time Turing machines (\ITTM s),…
In this paper, we introduce an achievability bound on the frame error rate of random tree code ensembles under a sequential decoding algorithm with a hard computational limit and consider the optimization of the random tree code ensembles…
Local Computation Algorithms (LCA), as introduced by Rubinfeld, Tamir, Vardi, and Xie (2011), are a type of ultra-efficient algorithms which, given access to a (large) input for a given computational task, are required to provide fast query…
The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is…
This paper presents finite-blocklength achievability bounds for the Gaussian multiple access channel (MAC) and random access channel (RAC) under average-error and maximal-power constraints. Using random codewords uniformly distributed on a…
Tensors are a fundamental operation in distributed computing, \emph{e.g.,} machine learning, that are commonly distributed into multiple parallel tasks for large datasets. Stragglers and other failures can severely impact the overall…
This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making novel use of a continuously specified Gaussian random field. We show that for…
Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper-bounding the average…
Distributed matrix computations -- matrix-matrix or matrix-vector multiplications -- are well-recognized to suffer from the problem of stragglers (slow or failed worker nodes). Much of prior work in this area is (i) either sub-optimal in…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
Given a single observation from a Gaussian distribution with unknown mean $\theta$, we design computationally efficient procedures that can approximately generate an observation from a different target distribution $Q_{\theta}$ uniformly…
We study the problem of universal decoding for unknown discrete memoryless channels in the presence of erasure/list option at the decoder, in the random coding regime. Specifically, we harness a universal version of Forney's classical…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting error probability as…