Identifying predictive factors via multivariable statistical analysis is for rare diseases often impossible because the data sets available are too small. Combining data from different medical centers into a single (larger) database would alleviate this problem, but is in practice challenging due to regulatory and logistic problems. Federated Learning (FL) is a machine learning approach that aims to construct from local inferences in separate data centers what would have been inferred had the data sets been merged. It seeks to harvest the statistical power of larger data sets without actually creating them. The FL strategy is not always feasible for small data sets. Therefore, in this paper we refine and implement an alternative Bayesian Federated Inference (BFI) framework for multi center data with the same aim as FL. The BFI framework is designed to cope with small data sets by inferring locally not only the optimal parameter values, but also additional features of the posterior parameter distribution, capturing information beyond that is used in FL. BFI has the additional benefit that a single inference cycle across the centers is sufficient, whereas FL needs multiple cycles. We quantify the performance of the proposed methodology on simulated and real life data.

Underdamped Langevin Monte Carlo (ULMC) is an algorithm used to sample from unnormalized densities by leveraging the momentum of a particle moving in a potential well. We provide a novel analysis of ULMC, motivated by two central questions: (1) Can we obtain improved sampling guarantees beyond strong log-concavity? (2) Can we achieve acceleration for sampling? For (1), prior results for ULMC only hold under a log-Sobolev inequality together with a restrictive Hessian smoothness condition. Here, we relax these assumptions by removing the Hessian smoothness condition and by considering distributions satisfying a Poincar\'e inequality. Our analysis achieves the state of art dimension dependence, and is also flexible enough to handle weakly smooth potentials. As a byproduct, we also obtain the first KL divergence guarantees for ULMC without Hessian smoothness under strong log-concavity, which is based on a new result on the log-Sobolev constant along the underdamped Langevin diffusion. For (2), the recent breakthrough of Cao, Lu, and Wang (2020) established the first accelerated result for sampling in continuous time via PDE methods. Our discretization analysis translates their result into an algorithmic guarantee, which indeed enjoys better condition number dependence than prior works on ULMC, although we leave open the question of full acceleration in discrete time. Both (1) and (2) necessitate R\'enyi discretization bounds, which are more challenging than the typically used Wasserstein coupling arguments. We address this using a flexible discretization analysis based on Girsanov's theorem that easily extends to more general settings.

There is a growing interest in the machine learning community in developing predictive algorithms that are "interpretable by design". Towards this end, recent work proposes to make interpretable decisions by sequentially asking interpretable queries about data until a prediction can be made with high confidence based on the answers obtained (the history). To promote short query-answer chains, a greedy procedure called Information Pursuit (IP) is used, which adaptively chooses queries in order of information gain. Generative models are employed to learn the distribution of query-answers and labels, which is in turn used to estimate the most informative query. However, learning and inference with a full generative model of the data is often intractable for complex tasks. In this work, we propose Variational Information Pursuit (V-IP), a variational characterization of IP which bypasses the need for learning generative models. V-IP is based on finding a query selection strategy and a classifier that minimizes the expected cross-entropy between true and predicted labels. We then demonstrate that the IP strategy is the optimal solution to this problem. Therefore, instead of learning generative models, we can use our optimal strategy to directly pick the most informative query given any history. We then develop a practical algorithm by defining a finite-dimensional parameterization of our strategy and classifier using deep networks and train them end-to-end using our objective. Empirically, V-IP is 10-100x faster than IP on different Vision and NLP tasks with competitive performance. Moreover, V-IP finds much shorter query chains when compared to reinforcement learning which is typically used in sequential-decision-making problems. Finally, we demonstrate the utility of V-IP on challenging tasks like medical diagnosis where the performance is far superior to the generative modelling approach.

We study the problem of uncertainty quantification via prediction sets, in an online setting where the data distribution may vary arbitrarily over time. Recent work develops online conformal prediction techniques that leverage regret minimization algorithms from the online learning literature to learn prediction sets with approximately valid coverage and small regret. However, standard regret minimization could be insufficient for handling changing environments, where performance guarantees may be desired not only over the full time horizon but also in all (sub-)intervals of time. We develop new online conformal prediction methods that minimize the strongly adaptive regret, which measures the worst-case regret over all intervals of a fixed length. We prove that our methods achieve near-optimal strongly adaptive regret for all interval lengths simultaneously, and approximately valid coverage. Experiments show that our methods consistently obtain better coverage and smaller prediction sets than existing methods on real-world tasks, such as time series forecasting and image classification under distribution shift.

We prove that various stochastic gradient descent methods, including the stochastic gradient descent (SGD), stochastic heavy-ball (SHB), and stochastic Nesterov's accelerated gradient (SNAG) methods, almost surely avoid any strict saddle manifold. To the best of our knowledge, this is the first time such results are obtained for SHB and SNAG methods. Moreover, our analysis expands upon previous studies on SGD by removing the need for bounded gradients of the objective function and uniformly bounded noise. Instead, we introduce a more practical local boundedness assumption for the noisy gradient, which is naturally satisfied in empirical risk minimization problems typically seen in training of neural networks. Keywords: Stochastic gradient descent, stochastic heavy-ball, stochastic Nesterov's accelerated gradient, almost sure saddle avoidance

Knowledge tracing (KT) serves as a primary part of intelligent education systems. Most current KTs either rely on expert judgments or only exploit a single network structure, which affects the full expression of learning features. To adequately mine features of students' learning process, Deep Knowledge Tracing Based on Spatial and Temporal Deep Representation Learning for Learning Performance Prediction (DKT-STDRL) is proposed in this paper. DKT-STDRL extracts spatial features from students' learning history sequence, and then further extracts temporal features to extract deeper hidden information. Specifically, firstly, the DKT-STDRL model uses CNN to extract the spatial feature information of students' exercise sequences. Then, the spatial features are connected with the original students' exercise features as joint learning features. Then, the joint features are input into the BiLSTM part. Finally, the BiLSTM part extracts the temporal features from the joint learning features to obtain the prediction information of whether the students answer correctly at the next time step. Experiments on the public education datasets ASSISTment2009, ASSISTment2015, Synthetic-5, ASSISTchall, and Statics2011 prove that DKT-STDRL can achieve better prediction effects than DKT and CKT.

The increasing use of Machine Learning (ML) software can lead to unfair and unethical decisions, thus fairness bugs in software are becoming a growing concern. Addressing these fairness bugs often involves sacrificing ML performance, such as accuracy. To address this issue, we present a novel counterfactual approach that uses counterfactual thinking to tackle the root causes of bias in ML software. In addition, our approach combines models optimized for both performance and fairness, resulting in an optimal solution in both aspects. We conducted a thorough evaluation of our approach on 10 benchmark tasks using a combination of 5 performance metrics, 3 fairness metrics, and 15 measurement scenarios, all applied to 8 real-world datasets. The conducted extensive evaluations show that the proposed method significantly improves the fairness of ML software while maintaining competitive performance, outperforming state-of-the-art solutions in 84.6% of overall cases based on a recent benchmarking tool.

An evident challenge ahead for the integrated circuit (IC) industry in the nanometer regime is the investigation and development of methods that can reduce the design complexity ensuing from growing process variations and curtail the turnaround time of chip manufacturing. Conventional methodologies employed for such tasks are largely manual; thus, time-consuming and resource-intensive. In contrast, the unique learning strategies of artificial intelligence (AI) provide numerous exciting automated approaches for handling complex and data-intensive tasks in very-large-scale integration (VLSI) design and testing. Employing AI and machine learning (ML) algorithms in VLSI design and manufacturing reduces the time and effort for understanding and processing the data within and across different abstraction levels via automated learning algorithms. It, in turn, improves the IC yield and reduces the manufacturing turnaround time. This paper thoroughly reviews the AI/ML automated approaches introduced in the past towards VLSI design and manufacturing. Moreover, we discuss the scope of AI/ML applications in the future at various abstraction levels to revolutionize the field of VLSI design, aiming for high-speed, highly intelligent, and efficient implementations.

The message passing-based graph neural networks (GNNs) have achieved great success in many real-world applications. However, training GNNs on large-scale graphs suffers from the well-known neighbor explosion problem, i.e., the exponentially increasing dependencies of nodes with the number of message passing layers. Subgraph-wise sampling methods--a promising class of mini-batch training techniques--discard messages outside the mini-batches in backward passes to avoid the neighbor explosion problem at the expense of gradient estimation accuracy. This poses significant challenges to their convergence analysis and convergence speeds, which seriously limits their reliable real-world applications. To address this challenge, we propose a novel subgraph-wise sampling method with a convergence guarantee, namely Local Message C ompensation (LMC). To the best of our knowledge, LMC is the first subgraph-wise sampling method with provable convergence. The key idea of LMC is to retrieve the discarded messages in backward passes based on a message passing formulation of backward passes. By efficient and effective compensations for the discarded messages in both forward and backward passes, LMC computes accurate mini-batch gradients and thus accelerates convergence. Experiments on large-scale benchmark tasks demonstrate that LMC significantly outperforms state-of-the-art subgraph-wise sampling methods in terms of efficiency. Graph neural networks (GNNs) are powerful frameworks that generate node embeddings for graphs via the iterative message passing (MP) scheme (Hamilton, 2020). At each MP layer, GNNs aggregate messages from each node's neighborhood and then update node embeddings based on aggregation results. Such a scheme has achieved great success in many real-world applications involving graph-structured data, such as search engines (Brin & Page, 1998), recommendation systems (Fan et al., 2019), materials engineering (Gostick et al., 2016), and molecular property prediction (Moloi & Ali, 2005; Kearnes et al., 2016).

We apply the PAC-Bayes theory to the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-bounds) and explicit trade-off between a high probability of convergence and a high convergence speed. Even in the limit case, where convergence is guaranteed, our learned optimization algorithms provably outperform related algorithms based on a (deterministic) worst-case analysis. Our results rely on PAC-Bayes bounds for general, unbounded loss-functions based on exponential families. By generalizing existing ideas, we reformulate the learning procedure into a one-dimensional minimization problem and study the possibility to find a global minimum, which enables the algorithmic realization of the learning procedure. As a proof-of-concept, we learn hyperparameters of standard optimization algorithms to empirically underline our theory.