Abstract: Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be highly useful to deal with this problem. We describe two quantum algorithms to efficiently fit scattered data based on globally and compactly supported RBFs respectively. For the globally supported RBF method, the core of the quantum algorithm relies on using coherent states to calculate the radial functions and a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion. A quadratic speedup is achieved in the number of data over the classical algorithms.

One major issue in learning-based model predictive control (MPC) for autonomous driving is the contradiction between the system model's prediction accuracy and computation efficiency. The more situations a system model covers, the more complex it is, along with highly nonlinear and nonconvex properties. These issues make the optimization too complicated to solve and render real-time control impractical.To address these issues, we propose a hierarchical learning residual model which leverages random forests and linear regression.The learned model consists of two levels. The low level uses linear regression to fit the residues, and the high level uses random forests to switch different linear models. Meanwhile, we adopt the linear dynamic bicycle model with error states as the nominal model.The switched linear regression model is added to the nominal model to form the system model. It reformulates the learning-based MPC as a quadratic program (QP) problem and optimization solvers can effectively solve it. Experimental path tracking results show that the driving vehicle's prediction accuracy and tracking accuracy are significantly improved compared with the nominal MPC.Compared with the state-of-the-art Gaussian process-based nonlinear model predictive control (GP-NMPC), our method gets better performance on tracking accuracy while maintaining a lower computation consumption.

Missing data in time series is a challenging issue affecting time series analysis. Missing data occurs due to problems like data drops or sensor malfunctioning. Imputation methods are used to fill in these values, with quality of imputation having a significant impact on downstream tasks like classification. In this work, we propose a semi-supervised imputation method, ST-Impute, that uses both unlabeled data along with downstream task's labeled data. ST-Impute is based on sparse self-attention and trains on tasks that mimic the imputation process. Our results indicate that the proposed method outperforms the existing supervised and unsupervised time series imputation methods measured on the imputation quality as well as on the downstream tasks ingesting imputed time series.

We consider distributed learning scenarios where M machines interact with a parameter server along several communication rounds in order to minimize a joint objective function. Focusing on the heterogeneous case, where different machines may draw samples from different data-distributions, we design the first local update method that provably benefits over the two most prominent distributed baselines: namely Minibatch-SGD and Local-SGD. Key to our approach is a slow querying technique that we customize to the distributed setting, which in turn enables a better mitigation of the bias caused by local updates.

We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of momentum. Then, we design an SGD-style algorithm as well as an accelerated version that make use of this new estimator, and demonstrate the robustness of these new approaches to the choice of the learning rate. Concretely, we show that these approaches obtain the optimal convergence rates for both noiseless and noisy case with the same choice of fixed learning rate. Moreover, for the noisy case we show that these approaches achieve the same optimal bound for a very wide range of learning rates.

With the rising complexity of numerous novel applications that serve our modern society comes the strong need to design efficient computing platforms. Designing efficient hardware is, however, a complex multi-objective problem that deals with multiple parameters and their interactions. Given that there are a large number of parameters and objectives involved in hardware design, synthesizing all possible combinations is not a feasible method to find the optimal solution. One promising approach to tackle this problem is statistical modeling of a desired hardware performance. Here, we propose a model-based active learning approach to solve this problem. Our proposed method uses Bayesian models to characterize various aspects of hardware performance. We also use transfer learning and Gaussian regression bootstrapping techniques in conjunction with active learning to create more accurate models. Our proposed statistical modeling method provides hardware models that are sufficiently accurate to perform design space exploration as well as performance prediction simultaneously. We use our proposed method to perform design space exploration and performance prediction for various hardware setups, such as micro-architecture design and OpenCL kernels for FPGA targets. Our experiments show that the number of samples required to create performance models significantly reduces while maintaining the predictive power of our proposed statistical models. For instance, in our performance prediction setting, the proposed method needs 65% fewer samples to create the model, and in the design space exploration setting, our proposed method can find the best parameter settings by exploring less than 50 samples.

Devising a fair classifier that does not discriminate against different groups is an important problem in machine learning. Recently, effort-based fairness notions are getting attention, which considers the scenarios of each individual making effort to improve its feature over time. Such scenarios happen in the real world, e.g., college admission and credit loaning, where each rejected sample makes effort to change its features to get accepted afterward. In this paper, we propose a new effortbased fairness notion called Equal Improvability (EI), which equalizes the potential acceptance rate of the rejected samples across different groups assuming a bounded level of effort will be spent by each rejected sample. We also propose and study three different approaches for finding a classifier that satisfies the EI requirement. Through experiments on both synthetic and real datasets, we demonstrate that the proposed EI-regularized algorithms encourage us to find a fair classifier in terms of EI. Additionally, we ran experiments on dynamic scenarios which highlight the advantages of our EI metric in equalizing the distribution of features across different groups, after the rejected samples make some effort to improve. Finally, we provide mathematical analyses of several aspects of EI: the relationship between EI and existing fairness notions, and the effect of EI in dynamic scenarios. Over the past decade, machine learning has been used in a wide variety of applications. However, these machine learning approaches are observed to be unfair to individuals having different ethnicity, race, and gender. As the implicit bias in artificial intelligence tools raised concerns over potential discrimination and equity issues, various researchers suggested defining fairness notions and developing classifiers that achieve fairness. One popular fairness notion is demographic parity (DP), which requires the decision-making system to provide output such that the groups are equally likely to be assigned to the desired prediction classes, e.g., acceptance in the admission procedure. DP and related fairness notions are largely employed to mitigate the bias in many realistic problems such as recruitment, credit lending, and university admissions (Zafar et al., 2017b; Hardt et al., 2016; Dwork et al., 2012; Zafar et al., 2017a). However, most of the existing fairness notions only focus on immediate fairness, without taking potential follow-up inequity risk into consideration.

Data-driven soft sensors are extensively used in industrial and chemical processes to predict hard-to-measure process variables whose real value is difficult to track during routine operations. The regression models used by these sensors often require a large number of labeled examples, yet obtaining the label information can be very expensive given the high time and cost required by quality inspections. In this context, active learning methods can be highly beneficial as they can suggest the most informative labels to query. However, most of the active learning strategies proposed for regression focus on the offline setting. In this work, we adapt some of these approaches to the stream-based scenario and show how they can be used to select the most informative data points. We also demonstrate how to use a semi-supervised architecture based on orthogonal autoencoders to learn salient features in a lower dimensional space. The Tennessee Eastman Process is used to compare the predictive performance of the proposed approaches.

A current goal in the graph neural network literature is to enable transformers to operate on graph-structured data, given their success on language and vision tasks. Since the transformer's original sinusoidal position encodings (PEs) are not applicable to graphs, recent work has focused on developing graph PEs, rooted in spectral graph theory or various spatial features of a graph. In this work, we introduce a new graph PE, Graph Automaton PE (GAPE), based on weighted graph-walking automata (a novel extension of graph-walking automata). We compare the performance of GAPE with other PE schemes on both machine translation and graph-structured tasks, and we show that it generalizes and connects with several other PEs. An additional contribution of this study is a theoretical and controlled experimental comparison of many recent PEs in graph transformers, independent of the use of edge features.

To model the Task 3 (Piskorski et al., 2023) expects the participants features representation of news articles across different to develop algorithms to automatically detect languages, the XLM-RoBERTa (XLM-R) the news genre, framing and persuasion techniques (Conneau et al., 2020) is fine-tuned since it can in a multilingual setup as shown in Table 1. Six different processes all the languages existing in Task 3, and languages are covered in this task, including typically outperforms other models such as mBERT English, French, German, Italian, Polish and Russian. (Kenton and Toutanova, 2019). In addition, three surprise languages, Spanish, In addition, this study also calculates the sample Greek and Georgian, are also included in the final weights and class weights to combat the data test phase for conducting a zero-shot learning imbalance. The sample weights enable a training scenario.