Rafał Wiśniewski

Qiongxiu Li, Jaron Skovsted Gundersen, Katrine Tjell et al.

Privacy has become a major concern in machine learning. In fact, the federated learning is motivated by the privacy concern as it does not allow to transmit the private data but only intermediate updates. However, federated learning does not always guarantee privacy-preservation as the intermediate updates may also reveal sensitive information. In this paper, we give an explicit information-theoretical analysis of a federated expectation maximization algorithm for Gaussian mixture model and prove that the intermediate updates can cause severe privacy leakage. To address the privacy issue, we propose a fully decentralized privacy-preserving solution, which is able to securely compute the updates in each maximization step. Additionally, we consider two different types of security attacks: the honest-but-curious and eavesdropping adversary models. Numerical validation shows that the proposed approach has superior performance compared to the existing approach in terms of both the accuracy and privacy level.

Deividas Eringis, John Leth, Zheng-Hua Tan et al.

In this paper we derive a PAC-Bayesian-Like error bound for a class of stochastic dynamical systems with inputs, namely, for linear time-invariant stochastic state-space models (stochastic LTI systems for short). This class of systems is widely used in control engineering and econometrics, in particular, they represent a special case of recurrent neural networks. In this paper we 1) formalize the learning problem for stochastic LTI systems with inputs, 2) derive a PAC-Bayesian-Like error bound for such systems, 3) discuss various consequences of this error bound.

Kevin Wilkinghoff, Neelu Madan, Juan Miguel Valverde et al.

Anomaly detection aims to identify observations that deviate from expected behavior. Because anomalous events are inherently sparse, most frameworks are trained exclusively on normal data to learn a single reference model of normality. This implicitly assumes that normal behavior can be captured by a single, unconditional reference distribution. In practice, however, anomalies are often context-dependent: A specific observation may be normal under one operating condition, yet anomalous under another. As machine learning systems are deployed in dynamic and heterogeneous environments, these fixed-context assumptions introduce structural ambiguity, i.e., the inability to distinguish contextual variation from genuine abnormality under marginal modeling, leading to unstable performance and unreliable anomaly assessments. While modern sensing systems frequently collect multimodal data capturing complementary aspects of both system behavior and operating conditions, existing methods treat all data streams equally, without distinguishing contextual information from anomaly-relevant signals. As a result, abnormality is often evaluated without explicitly conditioning on operating conditions. We argue that multimodal anomaly detection should be reframed as a cross-modal contextual inference problem, in which modalities play asymmetric roles, separating context from observation, to define abnormality conditionally rather than relative to a single global reference. This perspective has implications for model design, evaluation protocols, and benchmark construction, and outline open research challenges toward robust, context-aware multimodal anomaly detection.

Rahul Misra, Rafał Wisniewski, Carsten Skovmose Kallesøe

We study optimality for the safety-constrained Markov decision process which is the underlying framework for safe reinforcement learning. Specifically, we consider a constrained Markov decision process (with finite states and finite actions) where the goal of the decision maker is to reach a target set while avoiding an unsafe set(s) with certain probabilistic guarantees. Therefore the underlying Markov chain for any control policy will be multichain since by definition there exists a target set and an unsafe set. The decision maker also has to be optimal (with respect to a cost function) while navigating to the target set. This gives rise to a multi-objective optimization problem. We highlight the fact that Bellman's principle of optimality may not hold for constrained Markov decision problems with an underlying multichain structure (as shown by the counterexample due to Haviv. We resolve the counterexample by formulating the aforementioned multi-objective optimization problem as a zero-sum game and thereafter construct an asynchronous value iteration scheme for the Lagrangian (similar to Shapley's algorithm). Finally, we consider the reinforcement learning problem for the same and construct a modified $Q$-learning algorithm for learning the Lagrangian from data. We also provide a lower bound on the number of iterations required for learning the Lagrangian and corresponding error bounds.

Abhijit Mazumdar, Rafal Wisniewski, Manuela L. Bujorianu

In this paper, we present an online reinforcement learning algorithm for constrained Markov decision processes with a safety constraint. Despite the necessary attention of the scientific community, considering stochastic stopping time, the problem of learning optimal policy without violating safety constraints during the learning phase is yet to be addressed. To this end, we propose an algorithm based on linear programming that does not require a process model. We show that the learned policy is safe with high confidence. We also propose a method to compute a safe baseline policy, which is central in developing algorithms that do not violate the safety constraints. Finally, we provide simulation results to show the efficacy of the proposed algorithm. Further, we demonstrate that efficient exploration can be achieved by defining a subset of the state-space called proxy set.

Bulut Kuskonmaz, Jaron Skovsted Gundersen, Rafal Wisniewski

Mutual information $I(X;Y)$ is a useful definition in information theory to estimate how much information the random variable $Y$ holds about the random variable $X$. One way to define the mutual information is by comparing the joint distribution of $X$ and $Y$ with the product of the marginals through the KL-divergence. If the two distributions are close to each other there will be almost no leakage of $X$ from $Y$ since the two variables are close to being independent. In the discrete setting the mutual information has the nice interpretation of how many bits $Y$ reveals about $X$ and if $I(X;Y)=H(X)$ (the Shannon entropy of $X$) then $X$ is completely revealed. However, in the continuous case we do not have the same reasoning. For instance the mutual information can be infinite in the continuous case. This fact enables us to try different metrics or divergences to define the mutual information. In this paper, we are evaluating different metrics or divergences such as Kullback-Liebler (KL) divergence, Wasserstein distance, Jensen-Shannon divergence and total variation distance to form alternatives to the mutual information in the continuous case. We deploy different methods to estimate or bound these metrics and divergences and evaluate their performances.

Deividas Eringis, John Leth, Zheng-Hua Tan et al.

In this short article, we showcase the derivation of the optimal (minimum error variance) estimator, when one part of the stochastic LTI system output is not measured but is able to be predicted from the measured system outputs. Similar derivations have been done before but not using state-space representation.

Deividas Eringis, John Leth, Zheng-Hua Tan et al.

In this paper we derive a PAC-Bayesian error bound for autonomous stochastic LTI state-space models. The motivation for deriving such error bounds is that they will allow deriving similar error bounds for more general dynamical systems, including recurrent neural networks. In turn, PACBayesian error bounds are known to be useful for analyzing machine learning algorithms and for deriving new ones.