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This paper is concerned with inference on the conditional mean of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias correction term based on the weighted residuals of the Lasso regression. The weights depend on estimates of the missingness probabilities (propensity scores) and solve a convex optimization program that trades off bias and variance optimally. Provided that the propensity scores can be consistently estimated, the proposed estimator is asymptotically normal and semi-parametrically efficient among all asymptotically linear estimators. The rate at which the propensity scores are consistent is essentially irrelevant, allowing us to estimate them via modern machine learning techniques. We validate the finite-sample performance of the proposed estimator through comparative simulation studies and the real-world problem of inferring the stellar masses of galaxies in the Sloan Digital Sky Survey.

Solving linear inverse problems plays a crucial role in numerous applications. Algorithm unfolding based, model-aware data-driven approaches have gained significant attention for effectively addressing these problems. Learned iterative soft-thresholding algorithm (LISTA) and alternating direction method of multipliers compressive sensing network (ADMM-CSNet) are two widely used such approaches, based on ISTA and ADMM algorithms, respectively. In this work, we study optimization guarantees, i.e., achieving near-zero training loss with the increase in the number of learning epochs, for finite-layer unfolded networks such as LISTA and ADMM-CSNet with smooth soft-thresholding in an over-parameterized (OP) regime. We achieve this by leveraging a modified version of the Polyak-Lojasiewicz, denoted PL$^*$, condition. Satisfying the PL$^*$ condition within a specific region of the loss landscape ensures the existence of a global minimum and exponential convergence from initialization using gradient descent based methods. Hence, we provide conditions, in terms of the network width and the number of training samples, on these unfolded networks for the PL$^*$ condition to hold. We achieve this by deriving the Hessian spectral norm of these networks. Additionally, we show that the threshold on the number of training samples increases with the increase in the network width. Furthermore, we compare the threshold on training samples of unfolded networks with that of a standard fully-connected feed-forward network (FFNN) with smooth soft-thresholding non-linearity. We prove that unfolded networks have a higher threshold value than FFNN. Consequently, one can expect a better expected error for unfolded networks than FFNN.

Domain adaptation of GANs is a problem of fine-tuning GAN models pretrained on a large dataset (e.g. StyleGAN) to a specific domain with few samples (e.g. painting faces, sketches, etc.). While there are many methods that tackle this problem in different ways, there are still many important questions that remain unanswered. In this paper, we provide a systematic and in-depth analysis of the domain adaptation problem of GANs, focusing on the StyleGAN model. We perform a detailed exploration of the most important parts of StyleGAN that are responsible for adapting the generator to a new domain depending on the similarity between the source and target domains. As a result of this study, we propose new efficient and lightweight parameterizations of StyleGAN for domain adaptation. Particularly, we show that there exist directions in StyleSpace (StyleDomain directions) that are sufficient for adapting to similar domains. For dissimilar domains, we propose Affine+ and AffineLight+ parameterizations that allows us to outperform existing baselines in few-shot adaptation while having significantly less training parameters. Finally, we examine StyleDomain directions and discover their many surprising properties that we apply for domain mixing and cross-domain image morphing. Source code can be found at //github.com/AIRI-Institute/StyleDomain.

This paper proposes a novel LiDAR-Inertial odometry (LIO), named SR-LIO, based on an iterated extended Kalman filter (iEKF) framework. We adapt the sweep reconstruction method, which segments and reconstructs raw input sweeps from spinning LiDAR to obtain reconstructed sweeps with higher frequency. We found that such method can effectively reduce the time interval for each iterated state update, improving the state estimation accuracy and enabling the usage of iEKF framework for fusing high-frequency IMU and low-frequency LiDAR. To prevent inaccurate trajectory caused by multiple distortion correction to a particular point, we further propose to perform distortion correction for each segment. Experimental results on four public datasets demonstrate that our SR-LIO outperforms all existing state-of-the-art methods on accuracy, and reducing the time interval of iterated state update via the proposed sweep reconstruction can improve the accuracy and frequency of estimated states. The source code of SR-LIO is publicly available for the development of the community.

CholeskyQR2 and shifted CholeskyQR3 are two state-of-the-art algorithms for computing tall-and-skinny QR factorizations since they attain high performance on current computer architectures. However, to guarantee stability, for some applications, CholeskyQR2 faces a prohibitive restriction on the condition number of the underlying matrix to factorize. Shifted CholeskyQR3 is stable but has $50\%$ more computational and communication costs than CholeskyQR2. In this paper, a randomized QR algorithm called Randomized Householder-Cholesky (\texttt{rand\_cholQR}) is proposed and analyzed. Using one or two random sketch matrices, it is proved that with high probability, its orthogonality error is bounded by a constant of the order of unit roundoff for any numerically full-rank matrix, and hence it is as stable as shifted CholeskyQR3. An evaluation of the performance of \texttt{rand\_cholQR} on a NVIDIA A100 GPU demonstrates that for tall-and-skinny matrices, \texttt{rand\_cholQR} with multiple sketch matrices is nearly as fast as, or in some cases faster than, CholeskyQR2. Hence, compared to CholeskyQR2, \texttt{rand\_cholQR} is more stable with almost no extra computational or memory cost, and therefore a superior algorithm both in theory and practice.

In this paper, we introduce and analyze a lowest-order locking-free weak Galerkin (WG) finite element scheme for the grad-div formulation of linear elasticity problems. The scheme uses linear functions in the interior of mesh elements and constants on edges (2D) or faces (3D), respectively, to approximate the displacement. An $H(div)$-conforming displacement reconstruction operator is employed to modify test functions in the right-hand side of the discrete form, in order to eliminate the dependence of the $Lam\acute{e}$ parameter $\lambda$ in error estimates, i.e., making the scheme locking-free. The method works without requiring $\lambda \|\nabla\cdot \mathbf{u}\|_1$ to be bounded. We prove optimal error estimates, independent of $\lambda$, in both the $H^1$-norm and the $L^2$-norm. Numerical experiments validate that the method is effective and locking-free.

The paper considers the possibility of fine-tuning Llama 2 large language model (LLM) for the disinformation analysis and fake news detection. For fine-tuning, the PEFT/LoRA based approach was used. In the study, the model was fine-tuned for the following tasks: analysing a text on revealing disinformation and propaganda narratives, fact checking, fake news detection, manipulation analytics, extracting named entities with their sentiments. The obtained results show that the fine-tuned Llama 2 model can perform a deep analysis of texts and reveal complex styles and narratives. Extracted sentiments for named entities can be considered as predictive features in supervised machine learning models.

Orthogonal time sequency multiplexing (OTSM) has been recently proposed as a single-carrier (SC) waveform offering similar bit error rate (BER) to multi-carrier orthogonal time frequency space (OTFS) modulation in doubly-spread channels under high mobilities; however, with much lower complexity making OTSM a promising candidate for low-power millimeter-wave (mmWave) vehicular communications in 6G wireless networks. In this paper, the performance of OTSM-based homodyne transceiver is explored under hardware impairments (HIs) including in-phase and quadrature imbalance (IQI), direct current offset (DCO), phase noise, power amplifier non-linearity, carrier frequency offset, and synchronization timing offset. First, the discrete-time baseband signal model is obtained in vector form under the mentioned HIs. Then, the system input-output relations are derived in time, delay-time, and delay-sequency (DS) domains in which the parameters of HIs are incorporated. Analytical studies demonstrate that noise stays white Gaussian and effective channel matrix is sparse in the DS domain under HIs. Also, DCO appears as a DC signal at receiver interfering with only the zero sequency over all delay taps in the DS domain; however, IQI redounds to self-conjugated fully-overlapping sequency interference. Simulation results reveal the fact that with no HI compensation (HIC), not only OTSM outperforms plain SC waveform but it performs close to uncompensated OTFS system; however, HIC is essentially needed for OTSM systems operating in mmWave and beyond frequency bands.

While large language models (LLMs) have demonstrated remarkable capabilities across a range of downstream tasks, a significant concern revolves around their propensity to exhibit hallucinations: LLMs occasionally generate content that diverges from the user input, contradicts previously generated context, or misaligns with established world knowledge. This phenomenon poses a substantial challenge to the reliability of LLMs in real-world scenarios. In this paper, we survey recent efforts on the detection, explanation, and mitigation of hallucination, with an emphasis on the unique challenges posed by LLMs. We present taxonomies of the LLM hallucination phenomena and evaluation benchmarks, analyze existing approaches aiming at mitigating LLM hallucination, and discuss potential directions for future research.

Answering questions that require reading texts in an image is challenging for current models. One key difficulty of this task is that rare, polysemous, and ambiguous words frequently appear in images, e.g., names of places, products, and sports teams. To overcome this difficulty, only resorting to pre-trained word embedding models is far from enough. A desired model should utilize the rich information in multiple modalities of the image to help understand the meaning of scene texts, e.g., the prominent text on a bottle is most likely to be the brand. Following this idea, we propose a novel VQA approach, Multi-Modal Graph Neural Network (MM-GNN). It first represents an image as a graph consisting of three sub-graphs, depicting visual, semantic, and numeric modalities respectively. Then, we introduce three aggregators which guide the message passing from one graph to another to utilize the contexts in various modalities, so as to refine the features of nodes. The updated nodes have better features for the downstream question answering module. Experimental evaluations show that our MM-GNN represents the scene texts better and obviously facilitates the performances on two VQA tasks that require reading scene texts.