We establish in-expectation and tail bounds on the generalization error of representation learning type algorithms. The bounds are in terms of the relative entropy between the distribution of the representations extracted from the training and "test'' datasets and a data-dependent symmetric prior, i.e., the Minimum Description Length (MDL) of the latent variables for the training and test datasets. Our bounds are shown to reflect the "structure" and "simplicity'' of the encoder and significantly improve upon the few existing ones for the studied model. We then use our in-expectation bound to devise a suitable data-dependent regularizer; and we investigate thoroughly the important question of the selection of the prior. We propose a systematic approach to simultaneously learning a data-dependent Gaussian mixture prior and using it as a regularizer. Interestingly, we show that a weighted attention mechanism emerges naturally in this procedure. Our experiments show that our approach outperforms the now popular Variational Information Bottleneck (VIB) method as well as the recent Category-Dependent VIB (CDVIB).

A client device which has access to$n$training data samples needs to obtain a statistical hypothesis or model W and then to send it to a remote server. The client and the server devices share some common randomness sequence as well as a prior on the hypothesis space. In this problem a suitable hypothesis or model$W$should meet two distinct design criteria simultaneously: (i) small (population) risk during the inference phase and (ii) small ‘complexity’ for it to be conveyed to the server with minimum communication cost. In this paper, we propose a joint training and source coding scheme with provable in-expectation guarantees, where the expectation is over the encoder's output message. Specifically, we show that by imposing a constraint on a suitable Kullback-Leibler divergence between the conditional distribution induced by a compressed learning model$\hat{W}$given$W$and the prior, one guarantees simultaneously small average empirical risk (aka training loss), small average generalization error and small average communication cost. We also consider a one-shot scenario in which the guarantees on the empirical risk and generalization error are obtained for every encoder's output message.

A major challenge in designing efficient statistical supervised learning algorithms is finding representations that perform well not only on available training samples but also on unseen data. While the study of representation learning has spurred much interest, most existing such approaches are heuristic; and very little is known about theoretical generalization guarantees. For example, the information bottleneck method seeks a good generalization by finding a minimal description of the input that is maximally informative about the label variable, where minimality and informativeness are both measured by Shannon’s mutual information. In this paper, we establish a compressibility framework that allows us to derive upper bounds on the generalization error of a representation learning algorithm in terms of the ``Minimum Description Length'' (MDL) of the labels or the latent variables (representations). Rather than the mutual information between the encoder’s input and the representation, which is often believed to reflect the algorithm’s generalization capability in the related literature but in fact, falls short of doing so, our new bounds involve the "multi-letter" relative entropy between the distribution of the representations (or labels) of the training and test sets and a fixed prior. In particular, these new bounds reflect the structure of the encoder and are not vacuous for deterministic algorithms. Our compressibility approach, which is information-theoretic in nature, builds upon that of Blum-Langford for PAC-MDL bounds and introduces two essential ingredients: block-coding and lossy-compression. The latter allows our approach to subsume the so-called geometrical compressibility as a special case. To the best knowledge of the authors, the established generalization bounds are the first of their kind for Information Bottleneck type encoders and representation learning. Finally, we partly exploit the theoretical results by introducing a new data-dependent prior. Numerical simulations illustrate the advantages of well-chosen such priors over classical priors used in IB.

The current increasing need for privacy-preserving voice communications is leading to new ideas for securing voice transmission. This paper refers to a relatively new concept of sending encrypted speech as pseudo-speech in the audio domain over digital voice communication infrastructures, like 3G cellular network and VoIP. This work presents a novel distortion-tolerant speech encryption scheme for secure voice communications over voice channels that combines the robustness of analog speech scrambling and elevated security offered by digital ciphers like AES-CTR. The system scrambles vocal parameters of a speech signal (loudness, pitch, timbre) using distance-preserving pseudo-random translations and rotations on a hypersphere of parameters. Next, scrambled parameters are encoded to a pseudo-speech signal adapted to transmission over digital voice channels equipped with voice activity detection. Upon reception of this pseudo-speech signal, the legitimate receiver restores distorted copies of the initial vocal parameters. Despite some deciphering errors, an integrated neural-based vocoder based on the LPCNet architecture reconstructs an intelligible speech. The experimental implementation of this speech encryption scheme has been tested by simulations and sending an encrypted signal over FaceTime between two iPhones 6 connected to the same WiFi network. Moreover, speech excerpts restored from encrypted signals were evaluated by a speech quality assessment on a group of about 40 participants. The experiments demonstrated that the proposed scheme produces intelligible speech with a gracefully progressive quality degradation depending on the channel noise. Finally, the preliminary computational analysis suggested that the presented setting may operate on high-end portable devices in nearly real-time.

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