Multi-access Edge Computing (MEC) can be implemented together with Open Radio Access Network (O-RAN) over commodity platforms to offer low-cost deployment and bring the services closer to end-users. In this paper, a joint O-RAN/MEC orchestration using a Bayesian deep reinforcement learning (RL)-based framework is proposed that jointly controls the O-RAN functional splits, the allocated resources and hosting locations of the O-RAN/MEC services across geo-distributed platforms, and the routing for each O-RAN/MEC data flow. The goal is to minimize the long-term overall network operation cost and maximize the MEC performance criterion while adapting possibly time-varying O-RAN/MEC demands and resource availability. This orchestration problem is formulated as Markov decision process (MDP). However, the system consists of multiple BSs that share the same resources and serve heterogeneous demands, where their parameters have non-trivial relations. Consequently, finding the exact model of the underlying system is impractical, and the formulated MDP renders in a large state space with multi-dimensional discrete action. To address such modeling and dimensionality issues, a novel model-free RL agent is proposed for our solution framework. The agent is built from Double Deep Q-network (DDQN) that tackles the large state space and is then incorporated with action branching, an action decomposition method that effectively addresses the multi-dimensional discrete action with linear increase complexity. Further, an efficient exploration-exploitation strategy under a Bayesian framework using Thomson sampling is proposed to improve the learning performance and expedite its convergence. Trace-driven simulations are performed using an O-RAN-compliant model. The results show that our approach is data-efficient (i.e., converges faster) and increases the returned reward by 32\% than its non-Bayesian version.

Machine learning and data mining techniques are utiized for enhancement of the security of any network. Researchers used machine learning for pattern detection, anomaly detection, dynamic policy setting, etc. The methods allow the program to learn from data and make decisions without human intervention, consuming a huge training period and computation power. This paper discusses a novel technique to predict an upcoming attack in a network based on several data parameters. The dataset is continuous in real-time implementation. The proposed model comprises dataset pre-processing, and training, followed by the testing phase. Based on the results of the testing phase, the best model is selected using which, event class which may lead to an attack is extracted. The event statistics are used for attack

We study non-parametric density estimation for densities in Lipschitz and Sobolev spaces, and under central privacy. In particular, we investigate regimes where the privacy budget is not supposed to be constant. We consider the classical definition of central differential privacy, but also the more recent notion of central concentrated differential privacy. We recover the result of Barber \& Duchi (2014) stating that histogram estimators are optimal against Lipschitz distributions for the L2 risk, and under regular differential privacy, and we extend it to other norms and notions of privacy. Then, we investigate higher degrees of smoothness, drawing two conclusions: First, and contrary to what happens with constant privacy budget (Wasserman \& Zhou, 2010), there are regimes where imposing privacy degrades the regular minimax risk of estimation on Sobolev densities. Second, so-called projection estimators are near-optimal against the same classes of densities in this new setup with pure differential privacy, but contrary to the constant privacy budget case, it comes at the cost of relaxation. With zero concentrated differential privacy, there is no need for relaxation, and we prove that the estimation is optimal.

The challenge of producing accurate statistics while respecting the privacy of the individuals in a sample is an important area of research. We study minimax lower bounds for classes of differentially private estimators. In particular, we show how to characterize the power of a statistical test under differential privacy in a plug-and-play fashion by solving an appropriate transport problem. With specific coupling constructions, this observation allows us to derive Le Cam-type and Fano-type inequalities not only for regular definitions of differential privacy but also for those based on Renyi divergence. We then proceed to illustrate our results on three simple, fully worked out examples. In particular, we show that the problem class has a huge importance on the provable degradation of utility due to privacy. In certain scenarios, we show that maintaining privacy results in a noticeable reduction in performance only when the level of privacy protection is very high. Conversely, for other problems, even a modest level of privacy protection can lead to a significant decrease in performance. Finally, we demonstrate that the DP-SGLD algorithm, a private convex solver, can be employed for maximum likelihood estimation with a high degree of confidence, as it provides near-optimal results with respect to both the size of the sample and the level of privacy protection. This algorithm is applicable to a broad range of parametric estimation procedures, including exponential families.

With the significant successes of large language models (LLMs) in many natural language processing tasks, there is growing interest among researchers in exploring LLMs for novel recommender systems. However, we have observed that directly using LLMs as a recommender system is usually unstable due to its inherent position bias. To this end, we introduce exploratory research and find consistent patterns of positional bias in LLMs that influence the performance of recommendation across a range of scenarios. Then, we propose a Bayesian probabilistic framework, STELLA (Stable LLM for Recommendation), which involves a two-stage pipeline. During the first probing stage, we identify patterns in a transition matrix using a probing detection dataset. And in the second recommendation stage, a Bayesian strategy is employed to adjust the biased output of LLMs with an entropy indicator. Therefore, our framework can capitalize on existing pattern information to calibrate instability of LLMs, and enhance recommendation performance. Finally, extensive experiments clearly validate the effectiveness of our framework.

Graph contrastive learning (GCL) aims to align the positive features while differentiating the negative features in the latent space by minimizing a pair-wise contrastive loss. As the embodiment of an outstanding discriminative unsupervised graph representation learning approach, GCL achieves impressive successes in various graph benchmarks. However, such an approach falls short of recognizing the topology isomorphism of graphs, resulting in that graphs with relatively homogeneous node features cannot be sufficiently discriminated. By revisiting classic graph topology recognition works, we disclose that the corresponding expertise intuitively complements GCL methods. To this end, we propose a novel hierarchical topology isomorphism expertise embedded graph contrastive learning, which introduces knowledge distillations to empower GCL models to learn the hierarchical topology isomorphism expertise, including the graph-tier and subgraph-tier. On top of this, the proposed method holds the feature of plug-and-play, and we empirically demonstrate that the proposed method is universal to multiple state-of-the-art GCL models. The solid theoretical analyses are further provided to prove that compared with conventional GCL methods, our method acquires the tighter upper bound of Bayes classification error. We conduct extensive experiments on real-world benchmarks to exhibit the performance superiority of our method over candidate GCL methods, e.g., for the real-world graph representation learning experiments, the proposed method beats the state-of-the-art method by 0.23% on unsupervised representation learning setting, 0.43% on transfer learning setting. Our code is available at https://github.com/jyf123/HTML.

This work studies the learning process over social networks under partial and random information sharing. In traditional social learning models, agents exchange full belief information with each other while trying to infer the true state of nature. We study the case where agents share information about only one hypothesis, namely, the trending topic, which can be randomly changing at every iteration. We show that agents can learn the true hypothesis even if they do not discuss it, at rates comparable to traditional social learning. We also show that using one's own belief as a prior for estimating the neighbors' non-transmitted beliefs might create opinion clusters that prevent learning with full confidence. This phenomenon occurs when a single hypothesis corresponding to the truth is exchanged exclusively during all times. Such a practice, however, avoids the complete rejection of the truth under any information exchange procedure -- something that could happen if priors were uniform.

We propose a physics-informed machine learning method for uncertainty quantification in high-dimensional inverse problems. In this method, the states and parameters of partial differential equations (PDEs) are approximated with truncated conditional Karhunen-Lo\`eve expansions (CKLEs), which, by construction, match the measurements of the respective variables. The maximum a posteriori (MAP) solution of the inverse problem is formulated as a minimization problem over CKLE coefficients where the loss function is the sum of the norm of PDE residuals and the $\ell_2$ regularization term. This MAP formulation is known as the physics-informed CKLE (PICKLE) method. Uncertainty in the inverse solution is quantified in terms of the posterior distribution of CKLE coefficients, and we sample the posterior by solving a randomized PICKLE minimization problem, formulated by adding zero-mean Gaussian perturbations in the PICKLE loss function. We call the proposed approach the randomized PICKLE (rPICKLE) method. For linear and low-dimensional nonlinear problems (15 CKLE parameters), we show analytically and through comparison with Hamiltonian Monte Carlo (HMC) that the rPICKLE posterior converges to the true posterior given by the Bayes rule. For high-dimensional non-linear problems with 2000 CKLE parameters, we numerically demonstrate that rPICKLE posteriors are highly informative--they provide mean estimates with an accuracy comparable to the estimates given by the MAP solution and the confidence interval that mostly covers the reference solution. We are not able to obtain the HMC posterior to validate rPICKLE's convergence to the true posterior due to the HMC's prohibitive computational cost for the considered high-dimensional problems. Our results demonstrate the advantages of rPICKLE over HMC for approximately sampling high-dimensional posterior distributions subject to physics constraints.

This paper offers a fresh look at the pumping lemma constant as an upper bound for the finite structural information of a Context Free Grammar. An objective function based on indirect negative evidence considers the occurrences, and non-occurrences, of a finite number of trees, encountered after a sufficiently long non-adversial input presentation. This objective function has optimal substructure in the hypotheses space, giving rise to a greedy search learner. With this learner, a range of classes of Context Free Languages is shown to be learnable (identifiable in the limit) on an otherwise intractable hypotheses space.

Consider a single-product revenue-maximization problem where the seller monotonically decreases the price in $n$ rounds with an unknown demand model coming from a given family. Without monotonicity, the minimax regret is $\tilde O(n^{2/3})$ for the Lipschitz demand family and $\tilde O(n^{1/2})$ for a general class of parametric demand models. With monotonicity, the minimax regret is $\tilde O(n^{3/4})$ if the revenue function is Lipschitz and unimodal. However, the minimax regret for parametric families remained open. In this work, we provide a complete settlement for this fundamental problem. We introduce the crossing number to measure the complexity of a family of demand functions. In particular, the family of degree-$k$ polynomials has a crossing number $k$. Based on conservatism under uncertainty, we present (i) a policy with an optimal $\Theta(\log^2 n)$ regret for families with crossing number $k=0$, and (ii) another policy with an optimal $\tilde \Theta(n^{k/(k+1)})$ regret when $k\ge 1$. These bounds are asymptotically higher than the $\tilde O(\log n)$ and $\tilde \Theta(\sqrt n)$ minimax regret for the same families without the monotonicity constraint.