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Register a new userA Regression Approach to Certain Information Transmission Problems
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Added by
Wenyi Zhang
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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A general information transmission model, under independent and identically distributed Gaussian codebook and nearest neighbor decoding rule with processed channel output, is investigated using the performance metric of generalized mutual information. When the encoder and the decoder know the statistical channel model, it is found that the optimal channel output processing function is the conditional expectation operator, thus hinting a potential role of regression, a classical topic in machine learning, for this model. Without utilizing the statistical channel model, a problem formulation inspired by machine learning principles is established, with suitable performance metrics introduced. A data-driven inference algorithm is proposed to solve the problem, and the effectiveness of the algorithm is validated via numerical experiments. Extensions to more general information transmission models are also discussed.
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Scheduling the transmission of time-sensitive information from a source node to multiple users over error-prone communication channels is studied with the goal of minimizing the long-term average age of information (AoI) at the users. A long-term average resource constraint is imposed on the source, which limits the average number of transmissions. The source can transmit only to a single user at each time slot, and after each transmission, it receives an instantaneous ACK/NACK feedback from the intended receiver, and decides when and to which user to transmit the next update. Assuming the channel statistics are known, the optimal scheduling policy is studied for both the standard automatic repeat request (ARQ) and hybrid ARQ (HARQ) protocols. Then, a reinforcement learning(RL) approach is introduced to find a near-optimal policy, which does not assume any a priori information on the random processes governing the channel states. Different RL methods including average-cost SARSAwith linear function approximation (LFA), upper confidence reinforcement learning (UCRL2), and deep Q-network (DQN) are applied and compared through numerical simulations
Constraints on entropies are considered to be the laws of information theory. Even though the pursuit of their discovery has been a central theme of research in information theory, the algorithmic aspects of constraints on entropies remain largely unexplored. Here, we initiate an investigation of decision problems about constraints on entropies by placing several different such problems into levels of the arithmetical hierarchy. We establish the following results on checking the validity over all almost-entropic functions: first, validity of a Boolean information constraint arising from a monotone Boolean formula is co-recursively enumerable; second, validity of tight conditional information constraints is in $Pi^0_3$. Furthermore, under some restrictions, validity of conditional information constraints with slack is in $Sigma^0_2$, and validity of information inequality constraints involving max is Turing equivalent to validity of information inequality constraints (with no max involved). We also prove that the classical implication problem for conditional independence statements is co-recursively enumerable.
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It is commonly believed that the hidden layers of deep neural networks (DNNs) attempt to extract informative features for learning tasks. In this paper, we formalize this intuition by showing that the features extracted by DNN coincide with the result of an optimization problem, which we call the `universal feature selection problem, in a local analysis regime. We interpret the weights training in DNN as the projection of feature functions between feature spaces, specified by the network structure. Our formulation has direct operational meaning in terms of the performance for inference tasks, and gives interpretations to the internal computation results of DNNs. Results of numerical experiments are provided to support the analysis.
A new method to measure nonlinear dependence between two variables is described using mutual information to analyze the separate linear and nonlinear components of dependence. This technique, which gives an exact value for the proportion of linear dependence, is then compared with another common test for linearity, the Brock, Dechert and Scheinkman (BDS) test.
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