In this work, we propose methods for speeding up linear regression distributively, while ensuring security. We leverage randomized sketching techniques, and improve straggler resilience in asynchronous systems. Specifically, we apply a random orthonormal matrix and then subsample \textit{blocks}, to simultaneously secure the information and reduce the dimension of the regression problem. In our setup, the transformation corresponds to an encoded encryption in an \textit{approximate gradient coding scheme}, and the subsampling corresponds to the responses of the non-straggling workers; in a centralized coded computing network. This results in a distributive \textit{iterative sketching} approach for an $\ell_2$-subspace embedding, \textit{i.e.} a new sketch is considered at each iteration. We also focus on the special case of the \textit{Subsampled Randomized Hadamard Transform}, which we generalize to block sampling; and discuss how it can be modified in order to secure the data.

Reed-Muller (RM) codes achieve the capacity of general binary-input memoryless symmetric channels and are conjectured to have a comparable performance to that of random codes in terms of scaling laws. However, such results are established assuming maximum-likelihood decoders for general code parameters. Also, RM codes only admit limited sets of rates. Efficient decoders such as successive cancellation list (SCL) decoder and recently-introduced recursive projection-aggregation (RPA) decoders are available for RM codes at finite lengths. In this paper, we focus on subcodes of RM codes with flexible rates. We first extend the RPA decoding algorithm to RM subcodes. To lower the complexity of our decoding algorithm, referred to as subRPA, we investigate different approaches to prune the projections. Next, we derive the soft-decision based version of our algorithm, called soft-subRPA, that not only improves upon the performance of subRPA but also enables a differentiable decoding algorithm. Building upon the soft-subRPA algorithm, we then provide a framework for training a machine learning (ML) model to search for \textit{good} sets of projections that minimize the decoding error rate. Training our ML model enables achieving very close to the performance of full-projection decoding with a significantly smaller number of projections. We also show that the choice of the projections in decoding RM subcodes matters significantly, and our ML-aided projection pruning scheme is able to find a \textit{good} selection, i.e., with negligible performance degradation compared to the full-projection case, given a reasonable number of projections.

Federated learning (FL) is an emerging privacy-preserving paradigm, where a global model is trained at a central server while keeping client data local. However, FL can still indirectly leak private client information through model updates during training. Differential privacy (DP) can be employed to provide privacy guarantees within FL, typically at the cost of degraded final trained model. In this work, we consider a heterogeneous DP setup where clients are considered private by default, but some might choose to opt out of DP. We propose a new algorithm for federated learning with opt-out DP, referred to as \emph{FeO2}, along with a discussion on its advantages compared to the baselines of private and personalized FL algorithms. We prove that the server-side and client-side procedures in \emph{FeO2} are optimal for a simplified linear problem. We also analyze the incentive for opting out of DP in terms of performance gain. Through numerical experiments, we show that \emph{FeO2} provides up to $9.27\%$ performance gain in the global model compared to the baseline DP FL for the considered datasets. Additionally, we show a gap in the average performance of personalized models between non-private and private clients of up to $3.49\%$, empirically illustrating an incentive for clients to opt out.

Landmark codes underpin reliable physical layer communication, e.g., Reed-Muller, BCH, Convolution, Turbo, LDPC and Polar codes: each is a linear code and represents a mathematical breakthrough. The impact on humanity is huge: each of these codes has been used in global wireless communication standards (satellite, WiFi, cellular). Reliability of communication over the classical additive white Gaussian noise (AWGN) channel enables benchmarking and ranking of the different codes. In this paper, we construct KO codes, a computationaly efficient family of deep-learning driven (encoder, decoder) pairs that outperform the state-of-the-art reliability performance on the standardized AWGN channel. KO codes beat state-of-the-art Reed-Muller and Polar codes, under the low-complexity successive cancellation decoding, in the challenging short-to-medium block length regime on the AWGN channel. We show that the gains of KO codes are primarily due to the nonlinear mapping of information bits directly to transmit real symbols (bypassing modulation) and yet possess an efficient, high performance decoder. The key technical innovation that renders this possible is design of a novel family of neural architectures inspired by the computation tree of the {\bf K}ronecker {\bf O}peration (KO) central to Reed-Muller and Polar codes. These architectures pave way for the discovery of a much richer class of hitherto unexplored nonlinear algebraic structures. The code is available at \href{https://github.com/deepcomm/KOcodes}{https://github.com/deepcomm/KOcodes}

There are applications that may require removing the trace of a sample from the system, e.g., a user requests their data to be deleted, or corrupted data is discovered. Simply removing a sample from storage units does not necessarily remove its entire trace since downstream machine learning models may store some information about the samples used to train them. A sample can be perfectly unlearned if we retrain all models that used it from scratch with that sample removed from their training dataset. When multiple such unlearning requests are expected to be served, unlearning by retraining becomes prohibitively expensive. Ensemble learning enables the training data to be split into smaller disjoint shards that are assigned to non-communicating weak learners. Each shard is used to produce a weak model. These models are then aggregated to produce the final central model. This setup introduces an inherent trade-off between performance and unlearning cost, as reducing the shard size reduces the unlearning cost but may cause degradation in performance. In this paper, we propose a coded learning protocol where we utilize linear encoders to encode the training data into shards prior to the learning phase. We also present the corresponding unlearning protocol and show that it satisfies the perfect unlearning criterion. Our experimental results show that the proposed coded machine unlearning provides a better performance versus unlearning cost trade-off compared to the uncoded baseline.

We consider the critical problem of distributed learning over data while keeping it private from the computational servers. The state-of-the-art approaches to this problem rely on quantizing the data into a finite field, so that the cryptographic approaches for secure multiparty computing can then be employed. These approaches, however, can result in substantial accuracy losses due to fixed-point representation of the data and computation overflows. To address these critical issues, we propose a novel algorithm to solve the problem when data is in the analog domain, e.g., the field of real/complex numbers. We characterize the privacy of the data from both information-theoretic and cryptographic perspectives, while establishing a connection between the two notions in the analog domain. More specifically, the well-known connection between the distinguishing security (DS) and the mutual information security (MIS) metrics is extended from the discrete domain to the continues domain. This is then utilized to bound the amount of information about the data leaked to the servers in our protocol, in terms of the DS metric, using well-known results on the capacity of single-input multiple-output (SIMO) channel with correlated noise. It is shown how the proposed framework can be adopted to do computation tasks when data is represented using floating-point numbers. We then show that this leads to a fundamental trade-off between the privacy level of data and accuracy of the result. As an application, we also show how to train a machine learning model while keeping the data as well as the trained model private. Then numerical results are shown for experiments on the MNIST dataset. Furthermore, experimental advantages are shown comparing to fixed-point implementations over finite fields.

This paper models the crowdsourced labeling/classification problem as a sparsely encoded source coding problem, where each query answer, regarded as a code bit, is the XOR of a small number of labels, as source information bits. In this paper we leverage the connections between this problem and well-studied codes with sparse representations for the channel coding problem to provide querying schemes with almost optimal number of queries, each of which involving only a constant number of labels. We also extend this scenario to the case where some workers can be unresponsive. For this case, we propose querying schemes where each query involves only log n items, where n is the total number of items to be labeled. Furthermore, we consider classification of two correlated labeling systems and provide two-stage querying schemes with almost optimal number of queries each involving a constant number of labels.