Structural decomposition methods, such as generalized hypertree decompositions, have been successfully used for solving constraint satisfaction problems (CSPs). As decompositions can be reused to solve CSPs with the same constraint scopes, investing resources in computing good decompositions is beneficial, even though the computation itself is hard. Unfortunately, current methods need to compute a completely new decomposition even if the scopes change only slightly. In this paper, we make the first steps toward solving the problem of updating the decomposition of a CSP $P$ so that it becomes a valid decomposition of a new CSP $P'$ produced by some modification of $P$. Even though the problem is hard in theory, we propose and implement a framework for effectively updating GHDs. The experimental evaluation of our algorithm strongly suggests practical applicability.
The evaluation of clustering algorithms can involve running them on a variety of benchmark problems, and comparing their outputs to the reference, ground-truth groupings provided by experts. Unfortunately, many research papers and graduate theses consider only a small number of datasets. Also, the fact that there can be many equally valid ways to cluster a given problem set is rarely taken into account. In order to overcome these limitations, we have developed a framework whose aim is to introduce a consistent methodology for testing clustering algorithms. Furthermore, we have aggregated, polished, and standardised many clustering benchmark dataset collections referred to across the machine learning and data mining literature, and included new datasets of different dimensionalities, sizes, and cluster types. An interactive datasets explorer, the documentation of the Python API, a description of the ways to interact with the framework from other programming languages such as R or MATLAB, and other details are all provided at <https://clustering-benchmarks.gagolewski.com>.
Crowd sequential annotations can be an efficient and cost-effective way to build large datasets for sequence labeling. Different from tagging independent instances, for crowd sequential annotations the quality of label sequence relies on the expertise level of annotators in capturing internal dependencies for each token in the sequence. In this paper, we propose Modeling sequential annotation for sequence labeling with crowds (SA-SLC). First, a conditional probabilistic model is developed to jointly model sequential data and annotators' expertise, in which categorical distribution is introduced to estimate the reliability of each annotator in capturing local and non-local label dependency for sequential annotation. To accelerate the marginalization of the proposed model, a valid label sequence inference (VLSE) method is proposed to derive the valid ground-truth label sequences from crowd sequential annotations. VLSE derives possible ground-truth labels from the token-wise level and further prunes sub-paths in the forward inference for label sequence decoding. VLSE reduces the number of candidate label sequences and improves the quality of possible ground-truth label sequences. The experimental results on several sequence labeling tasks of Natural Language Processing show the effectiveness of the proposed model.
Real-time tracking of human body motion is crucial for interactive and immersive experiences in AR/VR. However, very limited sensor data about the body is available from standalone wearable devices such as HMDs (Head Mounted Devices) or AR glasses. In this work, we present a reinforcement learning framework that takes in sparse signals from an HMD and two controllers, and simulates plausible and physically valid full body motions. Using high quality full body motion as dense supervision during training, a simple policy network can learn to output appropriate torques for the character to balance, walk, and jog, while closely following the input signals. Our results demonstrate surprisingly similar leg motions to ground truth without any observations of the lower body, even when the input is only the 6D transformations of the HMD. We also show that a single policy can be robust to diverse locomotion styles, different body sizes, and novel environments.
Argument systems are based on the idea that one can construct arguments for propositions; i.e., structured reasons justifying the belief in a proposition. Using defeasible rules, arguments need not be valid in all circumstances, therefore, it might be possible to construct an argument for a proposition as well as its negation. When arguments support conflicting propositions, one of the arguments must be defeated, which raises the question of \emph{which (sub-)arguments can be subject to defeat}? In legal argumentation, meta-rules determine the valid arguments by considering the last defeasible rule of each argument involved in a conflict. Since it is easier to evaluate arguments using their last rules, \emph{can a conflict be resolved by considering only the last defeasible rules of the arguments involved}? We propose a new argument system where, instead of deriving a defeat relation between arguments, \emph{undercutting-arguments} for the defeat of defeasible rules are constructed. This system allows us, (\textit{i}) to resolve conflicts (a generalization of rebutting arguments) using only the last rules of the arguments for inconsistencies, (\textit{ii}) to determine a set of valid (undefeated) arguments in linear time using an algorithm based on a JTMS, (\textit{iii}) to establish a relation with Default Logic, and (\textit{iv}) to prove closure properties such as \emph{cumulativity}. We also propose an extension of the argument system that enables \emph{reasoning by cases}.
The click behavior is the most widely-used user positive feedback in recommendation. However, simply considering each click equally in training may suffer from clickbaits and title-content mismatching, and thus fail to precisely capture users' real satisfaction on items. Dwell time could be viewed as a high-quality quantitative indicator of user preferences on each click, while existing recommendation models do not fully explore the modeling of dwell time. In this work, we focus on reweighting clicks with dwell time in recommendation. Precisely, we first define a new behavior named valid read, which helps to select high-quality click instances for different users and items via dwell time. Next, we propose a normalized dwell time function to reweight click signals in training for recommendation. The Click reweighting model achieves significant improvements on both offline and online evaluations in real-world systems.
Reinforcement learning (RL) and trajectory optimization (TO) present strong complementary advantages. On one hand, RL approaches are able to learn global control policies directly from data, but generally require large sample sizes to properly converge towards feasible policies. On the other hand, TO methods are able to exploit gradient-based information extracted from simulators to quickly converge towards a locally optimal control trajectory which is only valid within the vicinity of the solution. Over the past decade, several approaches have aimed to adequately combine the two classes of methods in order to obtain the best of both worlds. Following on from this line of research, we propose several improvements on top of these approaches to learn global control policies quicker, notably by leveraging sensitivity information stemming from TO methods via Sobolev learning, and augmented Lagrangian techniques to enforce the consensus between TO and policy learning. We evaluate the benefits of these improvements on various classical tasks in robotics through comparison with existing approaches in the literature.
We consider the problem of synthesis of safe controllers for nonlinear systems with unknown dynamics using Control Barrier Functions (CBF). We utilize Koopman operator theory (KOT) to associate the (unknown) nonlinear system with a higher dimensional bilinear system and propose a data-driven learning framework that uses a learner and a falsifier to simultaneously learn the Koopman operator based bilinear system and a corresponding CBF. We prove that the learned CBF for the latter bilinear system is also a valid CBF for the unknown nonlinear system by characterizing the $\ell^2$-norm error bound between these two systems. We show that this error can be partially tuned by using the Lipschitz constant of the Koopman based observables. The CBF is then used to formulate a quadratic program to compute inputs that guarantee safety of the unknown nonlinear system. Numerical simulations are presented to validate our approach.
The optimal operation of regulated lakes is a challenging task involving conflicting objectives, ranging from controlling lake levels to avoid floods and low levels to water supply downstream. The traditional approach to operation policy design is based on an offline optimization, where a feedback control rule mapping lake storage into daily release decisions is identified over a set of observational data. In this paper, we propose a receding-horizon policy for a more frequent, online regulation of the lake level, and we discuss its tuning as compared to benchmark approaches. As side contributions, we provide a daily alternative based on the same rationale, and we show that this is still valid under some assumptions on the water inflow. Numerical simulations are used to show the effectiveness of the proposed approach. We demonstrate the approach on the regulated lake Como, Italy.
The rapid advancement of models based on artificial intelligence demands innovative monitoring techniques which can operate in real time with low computational costs. In machine learning, especially if we consider artificial neural networks (ANNs), the models are often trained in a supervised manner. Consequently, the learned relationship between the input and the output must remain valid during the model's deployment. If this stationarity assumption holds, we can conclude that the ANN provides accurate predictions. Otherwise, the retraining or rebuilding of the model is required. We propose considering the latent feature representation of the data (called "embedding") generated by the ANN to determine the time when the data stream starts being nonstationary. In particular, we monitor embeddings by applying multivariate control charts based on the data depth calculation and normalized ranks. The performance of the introduced method is compared with benchmark approaches for various ANN architectures and different underlying data formats.
Markov chain Monte Carlo (MCMC), such as Langevin dynamics, is valid for approximating intractable distributions. However, its usage is limited in the context of deep latent variable models owing to costly datapoint-wise sampling iterations and slow convergence. This paper proposes the amortized Langevin dynamics (ALD), wherein datapoint-wise MCMC iterations are entirely replaced with updates of an encoder that maps observations into latent variables. This amortization enables efficient posterior sampling without datapoint-wise iterations. Despite its efficiency, we prove that ALD is valid as an MCMC algorithm, whose Markov chain has the target posterior as a stationary distribution under mild assumptions. Based on the ALD, we also present a new deep latent variable model named the Langevin autoencoder (LAE). Interestingly, the LAE can be implemented by slightly modifying the traditional autoencoder. Using multiple synthetic datasets, we first validate that ALD can properly obtain samples from target posteriors. We also evaluate the LAE on the image generation task, and show that our LAE can outperform existing methods based on variational inference, such as the variational autoencoder, and other MCMC-based methods in terms of the test likelihood.
Strategy training is a multidisciplinary rehabilitation approach that teaches skills to reduce disability among those with cognitive impairments following a stroke. Strategy training has been shown in randomized, controlled clinical trials to be a more feasible and efficacious intervention for promoting independence than traditional rehabilitation approaches. A standardized fidelity assessment is used to measure adherence to treatment principles by examining guided and directed verbal cues in video recordings of rehabilitation sessions. Although the fidelity assessment for detecting guided and directed verbal cues is valid and feasible for single-site studies, it can become labor intensive, time consuming, and expensive in large, multi-site pragmatic trials. To address this challenge to widespread strategy training implementation, we leveraged natural language processing (NLP) techniques to automate the strategy training fidelity assessment, i.e., to automatically identify guided and directed verbal cues from video recordings of rehabilitation sessions. We developed a rule-based NLP algorithm, a long-short term memory (LSTM) model, and a bidirectional encoder representation from transformers (BERT) model for this task. The best performance was achieved by the BERT model with a 0.8075 F1-score. This BERT model was verified on an external validation dataset collected from a separate major regional health system and achieved an F1 score of 0.8259, which shows that the BERT model generalizes well. The findings from this study hold widespread promise in psychology and rehabilitation intervention research and practice.
Machine Learning models are prone to fail when test data are different from training data, a situation often encountered in real applications known as distribution shift. While still valid, the training-time knowledge becomes less effective, requiring a test-time adaptation to maintain high performance. Following approaches that assume batch-norm layer and use their statistics for adaptation, we propose a Test-Time Adaptation with Principal Component Analysis (TTAwPCA), which presumes a fitted PCA and adapts at test time a spectral filter based on the singular values of the PCA for robustness to corruptions. TTAwPCA combines three components: the output of a given layer is decomposed using a Principal Component Analysis (PCA), filtered by a penalization of its singular values, and reconstructed with the PCA inverse transform. This generic enhancement adds fewer parameters than current methods. Experiments on CIFAR-10-C and CIFAR- 100-C demonstrate the effectiveness and limits of our method using a unique filter of 2000 parameters.
In this paper, we consider testing the martingale difference hypothesis for high-dimensional time series. Our test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear dependence measure at different lags. To conduct the inference, we approximate the null distribution of our test statistic by Gaussian approximation and provide a simulation-based approach to generate critical values. The asymptotic behavior of the test statistic under the alternative is also studied. Our approach is nonparametric as the null hypothesis only assumes the time series concerned is martingale difference without specifying any parametric forms of its conditional moments. As an advantage of Gaussian approximation, our test is robust to the cross-series dependence of unknown magnitude. To the best of our knowledge, this is the first valid test for the martingale difference hypothesis that not only allows for large dimension but also captures nonlinear serial dependence. The practical usefulness of our test is illustrated via simulation and a real data analysis. The test is implemented in a user-friendly R-function.
This paper introduces a consistent estimator and rate of convergence for the precision matrix of asset returns in large portfolios using a non-linear factor model within the deep learning framework. Our estimator remains valid even in low signal-to-noise ratio environments typical for financial markets and is compatible with weak factors. Our theoretical analysis establishes uniform bounds on expected estimation risk based on deep neural networks for an expanding number of assets. Additionally, we provide a new consistent data-dependent estimator of error covariance in deep neural networks. Our models demonstrate superior accuracy in extensive simulations and the empirics.
We propose a method for estimation and inference for bounds for heterogeneous causal effect parameters in general sample selection models where the treatment can affect whether an outcome is observed and no exclusion restrictions are available. The method provides conditional effect bounds as functions of policy relevant pre-treatment variables. It allows for conducting valid statistical inference on the unidentified conditional effects. We use a flexible debiased/double machine learning approach that can accommodate non-linear functional forms and high-dimensional confounders. Easily verifiable high-level conditions for estimation, misspecification robust confidence intervals, and uniform confidence bands are provided as well. We re-analyze data from a large scale field experiment on Facebook on counter-attitudinal news subscription with attrition. Our method yields substantially tighter effect bounds compared to conventional methods and suggests depolarization effects for younger users.
Lower bounds on the mean square error (MSE) play an important role in evaluating the direction-of-arrival (DOA) estimation performance. Among numerous bounds for DOA estimation, the local Cramer-Rao bound (CRB) is only tight asymptotically. By contrast, the existing global tight Ziv-Zakai bound (ZZB) is appropriate for evaluating the single source estimation only. In this paper, we derive an explicit ZZB applicable for evaluating hybrid coherent/incoherent multiple sources DOA estimation. It is first shown that, a straightforward generalization of ZZB from single source estimation to multiple sources estimation cannot keep the bound valid in the a priori performance region. To derive a global tight ZZB, we then introduce order statistics to describe the change of the a priori distribution of DOAs caused by ordering process during the MSE calculation. The derived ZZB is for the first time formulated as a function of coherent coefficients between coherent sources, and reveals the relationship between the MSE convergency in the a priori performance region and the number of sources. Moreover, the derived ZZB also provides a unified tight bound for both overdetermined and underdetermined DOA estimation. Simulation results demonstrate the obvious advantages of the derived ZZB over the CRB on evaluating and predicting the estimation performance for multiple sources DOA.
This paper focuses on providing an analytical framework for the quantification and evaluation of the pointing error for a general case at high-frequency millimeter wave (mmWave) and terahertz (THz) communication links. For this aim, we first derive the the probability density function (PDF) and cumulative distribution functions (CDF) of the pointing error between an unstable transmitter (Tx) and receiver (Rx), that have different antenna patterns and for which the vibrations are not similar in the Yaw and Pitch directions. The special case where the Tx and Rx are both equipped with uniform linear array antenna is also investigated. In addition, using $\alpha-\mu$ distribution, which is a valid model for small-scale fading of mmWave/THz links, the end-to-end PDF and CDF of the considered channel is derived for all the considered cases. Finally, by employing Monte-Carlo simulations, the accuracy of the analytical expressions is verified and the performance of the system is studied.
Millimeter wave (mmWave) radar sensors are emerging as valid alternatives to cameras for the pervasive contactless monitoring of people in indoor spaces. However, commercial mmWave radars feature a limited range (up to $6$-$8$ m) and are subject to occlusion, which may constitute a significant drawback in large, crowded rooms characterized by a challenging multipath environment. Thus, covering large indoor spaces requires multiple radars with known relative position and orientation and algorithms to combine their outputs. In this work, we present ORACLE, an autonomous system that (i) integrates automatic relative position and orientation estimation from multiple radar devices by exploiting the trajectories of people moving freely in the radars' common fields of view, and (ii) fuses the tracking information from multiple radars to obtain a unified tracking among all sensors. Our implementation and experimental evaluation of ORACLE results in median errors of $0.12$ m and $0.03^\circ$ for radars location and orientation estimates, respectively. Fused tracking improves the mean target tracking accuracy by $27\%$, and the mean tracking error is $23$ cm in the most challenging case of $3$ moving targets. Finally, ORACLE does not show significant performance reduction when the fusion rate is reduced to up to 1/5 of the frame rate of the single radar sensors, thus being amenable to a lightweight implementation on a resource-constrained fusion center.
Accurately annotated image datasets are essential components for studying animal behaviors from their poses. Compared to the number of species we know and may exist, the existing labeled pose datasets cover only a small portion of them, while building comprehensive large-scale datasets is prohibitively expensive. Here, we present a very data efficient strategy targeted for pose estimation in quadrupeds that requires only a small amount of real images from the target animal. It is confirmed that fine-tuning a backbone network with pretrained weights on generic image datasets such as ImageNet can mitigate the high demand for target animal pose data and shorten the training time by learning the the prior knowledge of object segmentation and keypoint estimation in advance. However, when faced with serious data scarcity (i.e., $<10^2$ real images), the model performance stays unsatisfactory, particularly for limbs with considerable flexibility and several comparable parts. We therefore introduce a prior-aware synthetic animal data generation pipeline called PASyn to augment the animal pose data essential for robust pose estimation. PASyn generates a probabilistically-valid synthetic pose dataset, SynAP, through training a variational generative model on several animated 3D animal models. In addition, a style transfer strategy is utilized to blend the synthetic animal image into the real backgrounds. We evaluate the improvement made by our approach with three popular backbone networks and test their pose estimation accuracy on publicly available animal pose images as well as collected from real animals in a zoo.