In the present work, we consider variable selection and shrinkage for the Gaussian dynamic linear regression within a Bayesian framework. In particular, we propose a novel method that allows for time-varying sparsity, based on an extension of spike-and-slab priors for dynamic models. This is done by assigning appropriate Markov switching priors for the time-varying coefficients' variances, extending the previous work of Ishwaran and Rao (2005). Furthermore, we investigate different priors, including the common Inverted gamma prior for the process variances, and other mixture prior distributions such as Gamma priors for both the spike and the slab, which leads to a mixture of Normal-Gammas priors (Griffin ad Brown, 2010) for the coefficients. In this sense, our prior can be view as a dynamic variable selection prior which induces either smoothness (through the slab) or shrinkage towards zero (through the spike) at each time point. The MCMC method used for posterior computation uses Markov latent variables that can assume binary regimes at each time point to generate the coefficients' variances. In that way, our model is a dynamic mixture model, thus, we could use the algorithm of Gerlach et al (2000) to generate the latent processes without conditioning on the states. Finally, our approach is exemplified through simulated examples and a real data application.

The Fr\'echet Inception Distance (FID) has been used to evaluate thousands of generative models. We present a novel algorithm, FastFID, which allows fast computation and backpropagation for FID. FastFID can efficiently (1) evaluate generative model *during* training and (2) construct adversarial examples for FID.

This work targets the identification of a class of models for hybrid dynamical systems characterized by nonlinear autoregressive exogenous (NARX) components, with finite-dimensional polynomial expansions, and by a Markovian switching mechanism. The estimation of the model parameters is performed under a probabilistic framework via Expectation Maximization, including submodel coefficients, hidden state values and transition probabilities. Discrete mode classification and NARX regression tasks are disentangled within the iterations. Soft-labels are assigned to latent states on the trajectories by averaging over the state posteriors and updated using the parametrization obtained from the previous maximization phase. Then, NARXs parameters are repeatedly fitted by solving weighted regression subproblems through a cyclical coordinate descent approach with coordinate-wise minimization. Moreover, we investigate a two stage selection scheme, based on a l1-norm bridge estimation followed by hard-thresholding, to achieve parsimonious models through selection of the polynomial expansion. The proposed approach is demonstrated on a SMNARX problem composed by three nonlinear sub-models with specific regressors.

We design a low complexity decentralized learning algorithm to train a recently proposed large neural network in distributed processing nodes (workers). We assume the communication network between the workers is synchronized and can be modeled as a doubly-stochastic mixing matrix without having any master node. In our setup, the training data is distributed among the workers but is not shared in the training process due to privacy and security concerns. Using alternating-direction-method-of-multipliers (ADMM) along with a layerwise convex optimization approach, we propose a decentralized learning algorithm which enjoys low computational complexity and communication cost among the workers. We show that it is possible to achieve equivalent learning performance as if the data is available in a single place. Finally, we experimentally illustrate the time complexity and convergence behavior of the algorithm.

Hybrid system identification is a key tool to achieve reliable models of Cyber-Physical Systems from data. PieceWise Affine models guarantees universal approximation, local linearity and equivalence to other classes of hybrid system. Still, PWA identification is a challenging problem, requiring the concurrent solution of regression and classification tasks. In this work, we focus on the identification of PieceWise Auto Regressive with eXogenous input models with arbitrary regions (NPWARX), thus not restricted to polyhedral domains, and characterized by discontinuous maps. To this end, we propose a method based on a probabilistic mixture model, where the discrete state is represented through a multinomial distribution conditioned by the input regressors. The architecture is conceived following the Mixture of Expert concept, developed within the machine learning field. To achieve nonlinear partitioning, we parametrize the discriminant function using a neural network. Then, the parameters of both the ARX submodels and the classifier are concurrently estimated by maximizing the likelihood of the overall model using Expectation Maximization. The proposed method is demonstrated on a nonlinear piece-wise problem with discontinuous maps.

Support Vector Data Description (SVDD) is a popular one-class classifiers for anomaly and novelty detection. But despite its effectiveness, SVDD does not scale well with data size. To avoid prohibitive training times, sampling methods select small subsets of the training data on which SVDD trains a decision boundary hopefully equivalent to the one obtained on the full data set. According to the literature, a good sample should therefore contain so-called boundary observations that SVDD would select as support vectors on the full data set. However, non-boundary observations also are essential to not fragment contiguous inlier regions and avoid poor classification accuracy. Other aspects, such as selecting a sufficiently representative sample, are important as well. But existing sampling methods largely overlook them, resulting in poor classification accuracy. In this article, we study how to select a sample considering these points. Our approach is to frame SVDD sampling as an optimization problem, where constraints guarantee that sampling indeed approximates the original decision boundary. We then propose RAPID, an efficient algorithm to solve this optimization problem. RAPID does not require any tuning of parameters, is easy to implement and scales well to large data sets. We evaluate our approach on real-world and synthetic data. Our evaluation is the most comprehensive one for SVDD sampling so far. Our results show that RAPID outperforms its competitors in classification accuracy, in sample size, and in runtime.

The effectiveness of traditional traffic prediction methods is often extremely limited when forecasting traffic dynamics in early morning. The reason is that traffic can break down drastically during the early morning commute, and the time and duration of this break-down vary substantially from day to day. Early morning traffic forecast is crucial to inform morning-commute traffic management, but they are generally challenging to predict in advance, particularly by midnight. In this paper, we propose to mine Twitter messages as a probing method to understand the impacts of people's work and rest patterns in the evening/midnight of the previous day to the next-day morning traffic. The model is tested on freeway networks in Pittsburgh as experiments. The resulting relationship is surprisingly simple and powerful. We find that, in general, the earlier people rest as indicated from Tweets, the more congested roads will be in the next morning. The occurrence of big events in the evening before, represented by higher or lower tweet sentiment than normal, often implies lower travel demand in the next morning than normal days. Besides, people's tweeting activities in the night before and early morning are statistically associated with congestion in morning peak hours. We make use of such relationships to build a predictive framework which forecasts morning commute congestion using people's tweeting profiles extracted by 5 am or as late as the midnight prior to the morning. The Pittsburgh study supports that our framework can precisely predict morning congestion, particularly for some road segments upstream of roadway bottlenecks with large day-to-day congestion variation. Our approach considerably outperforms those existing methods without Twitter message features, and it can learn meaningful representation of demand from tweeting profiles that offer managerial insights.

High-dimensional streaming data are becoming increasingly ubiquitous in many fields. They often lie in multiple low-dimensional subspaces, and the manifold structures may change abruptly on the time scale due to pattern shift or occurrence of anomalies. However, the problem of detecting the structural changes in a real-time manner has not been well studied. To fill this gap, we propose a dynamic sparse subspace learning (DSSL) approach for online structural change-point detection of high-dimensional streaming data. A novel multiple structural change-point model is proposed and it is shown to be equivalent to maximizing a posterior under certain conditions. The asymptotic properties of the estimators are investigated. The penalty coefficients in our model can be selected by AMDL criterion based on some historical data. An efficient Pruned Exact Linear Time (PELT) based method is proposed for online optimization and change-point detection. The effectiveness of the proposed method is demonstrated through a simulation study and a real case study using gesture data for motion tracking.

Transformers have been proven a successful model for a variety of tasks in sequence modeling. However, computing the attention matrix, which is their key component, has quadratic complexity with respect to the sequence length, thus making them prohibitively expensive for large sequences. To address this, we propose clustered attention, which instead of computing the attention for every query, groups queries into clusters and computes attention just for the centroids. To further improve this approximation, we use the computed clusters to identify the keys with the highest attention per query and compute the exact key/query dot products. This results in a model with linear complexity with respect to the sequence length for a fixed number of clusters. We evaluate our approach on two automatic speech recognition datasets and show that our model consistently outperforms vanilla transformers for a given computational budget. Finally, we demonstrate that our model can approximate arbitrarily complex attention distributions with a minimal number of clusters by approximating a pretrained BERT model on GLUE and SQuAD benchmarks with only 25 clusters and no loss in performance.

Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to underlying expansion of economy and evolution of demographics). This motivates understanding conditions on probability distributions, using the Wasserstein distance, that can be used to model time-varying environments. We can then use these conditions in conjunction with online stochastic optimization to adapt the decisions. We considers an online proximal-gradient method to track the minimizers of expectations of smooth convex functions parameterised by a random variable whose probability distributions continuously evolve over time at a rate similar to that of the rate at which the decision maker acts. We revisit the concepts of estimation and tracking error inspired by systems and control literature and provide bounds for them under strong convexity, Lipschitzness of the gradient, and bounds on the probability distribution drift. Further, noting that computing projections for a general feasible sets might not be amenable to online implementation (due to computational constraints), we propose an exact penalty method. Doing so allows us to relax the uniform boundedness of the gradient and establish dynamic regret bounds for tracking and estimation error. We further introduce a constraint-tightening approach and relate the amount of tightening to the probability of satisfying the constraints.