Feature-distributed data, referred to data partitioned by features and stored across multiple computing nodes, are increasingly common in applications with a large number of features. This paper proposes a two-stage relaxed greedy algorithm (TSRGA) for applying multivariate linear regression to such data. The main advantage of TSRGA is that its communication complexity does not depend on the feature dimension, making it highly scalable to very large data sets. In addition, for multivariate response variables, TSRGA can be used to yield low-rank coefficient estimates. The fast convergence of TSRGA is validated by simulation experiments. Finally, we apply the proposed TSRGA in a financial application that leverages unstructured data from the 10-K reports, demonstrating its usefulness in applications with many dense large-dimensional matrices.

Recent work has highlighted the label alignment property (LAP) in supervised learning, where the vector of all labels in the dataset is mostly in the span of the top few singular vectors of the data matrix. Drawing inspiration from this observation, we propose a regularization method for unsupervised domain adaptation that encourages alignment between the predictions in the target domain and its top singular vectors. Unlike conventional domain adaptation approaches that focus on regularizing representations, we instead regularize the classifier to align with the unsupervised target data, guided by the LAP in both the source and target domains. Theoretical analysis demonstrates that, under certain assumptions, our solution resides within the span of the top right singular vectors of the target domain data and aligns with the optimal solution. By removing the reliance on the commonly used optimal joint risk assumption found in classic domain adaptation theory, we showcase the effectiveness of our method on addressing problems where traditional domain adaptation methods often fall short due to high joint error. Additionally, we report improved performance over domain adaptation baselines in well-known tasks such as MNIST-USPS domain adaptation and cross-lingual sentiment analysis.

Neural sequence models based on the transformer architecture have demonstrated remarkable \emph{in-context learning} (ICL) abilities, where they can perform new tasks when prompted with training and test examples, without any parameter update to the model. This work first provides a comprehensive statistical theory for transformers to perform ICL. Concretely, we show that transformers can implement a broad class of standard machine learning algorithms in context, such as least squares, ridge regression, Lasso, learning generalized linear models, and gradient descent on two-layer neural networks, with near-optimal predictive power on various in-context data distributions. Using an efficient implementation of in-context gradient descent as the underlying mechanism, our transformer constructions admit mild size bounds, and can be learned with polynomially many pretraining sequences. Building on these ``base'' ICL algorithms, intriguingly, we show that transformers can implement more complex ICL procedures involving \emph{in-context algorithm selection}, akin to what a statistician can do in real life -- A \emph{single} transformer can adaptively select different base ICL algorithms -- or even perform qualitatively different tasks -- on different input sequences, without any explicit prompting of the right algorithm or task. We both establish this in theory by explicit constructions, and also observe this phenomenon experimentally. In theory, we construct two general mechanisms for algorithm selection with concrete examples: pre-ICL testing, and post-ICL validation. As an example, we use the post-ICL validation mechanism to construct a transformer that can perform nearly Bayes-optimal ICL on a challenging task -- noisy linear models with mixed noise levels. Experimentally, we demonstrate the strong in-context algorithm selection capabilities of standard transformer architectures.

This research proposes a machine learning-based attack detection model for power systems, specifically targeting smart grids. By utilizing data and logs collected from Phasor Measuring Devices (PMUs), the model aims to learn system behaviors and effectively identify potential security boundaries. The proposed approach involves crucial stages including dataset pre-processing, feature selection, model creation, and evaluation. To validate our approach, we used a dataset used, consist of 15 separate datasets obtained from different PMUs, relay snort alarms and logs. Three machine learning models: Random Forest, Logistic Regression, and K-Nearest Neighbour were built and evaluated using various performance metrics. The findings indicate that the Random Forest model achieves the highest performance with an accuracy of 90.56% in detecting power system disturbances and has the potential in assisting operators in decision-making processes.

Machine Learning requires a large amount of training data in order to build accurate models. Sometimes the data arrives over time, requiring significant storage space and recalculating the model to account for the new data. On-line learning addresses these issues by incrementally modifying the model as data is encountered, and then discarding the data. In this study we introduce a new online linear regression approach. Our approach combines newly arriving data with a previously existing model to create a new model. The introduced model, named OLR-WA (OnLine Regression with Weighted Average) uses user-defined weights to provide flexibility in the face of changing data to bias the results in favor of old or new data. We have conducted 2-D and 3-D experiments comparing OLR-WA to a static model using the entire data set. The results show that for consistent data, OLR-WA and the static batch model perform similarly and for varying data, the user can set the OLR-WA to adapt more quickly or to resist change.

Understanding interpersonal communication requires, in part, understanding the social context and norms in which a message is said. However, current methods for identifying offensive content in such communication largely operate independent of context, with only a few approaches considering community norms or prior conversation as context. Here, we introduce a new approach to identifying inappropriate communication by explicitly modeling the social relationship between the individuals. We introduce a new dataset of contextually-situated judgments of appropriateness and show that large language models can readily incorporate relationship information to accurately identify appropriateness in a given context. Using data from online conversations and movie dialogues, we provide insight into how the relationships themselves function as implicit norms and quantify the degree to which context-sensitivity is needed in different conversation settings. Further, we also demonstrate that contextual-appropriateness judgments are predictive of other social factors expressed in language such as condescension and politeness.

We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear in the dimension, and additive noise is assumed to be independent Gaussian with variance $\sigma^2$. Prior work has shown that the problem suffers from a $\frac{k}{SNR^2}$-to-$\frac{k^2}{SNR^2}$ statistical-to-computational gap, resembling other computationally challenging high-dimensional inference problems such as Sparse PCA and Robust Sparse Mean Estimation; here $SNR$ is the signal-to-noise ratio. We establish the existence of a more extensive computational barrier for this problem through the method of low-degree polynomials, but show that the problem is computationally hard only in a very narrow symmetric parameter regime. We identify a smooth information-computation tradeoff between the sample complexity $n$ and runtime for any randomized algorithm in this hard regime. Via a simple reduction, this provides novel rigorous evidence for the existence of a computational barrier to solving exact support recovery in sparse phase retrieval with sample complexity $n = \tilde{o}(k^2)$. Our second contribution is to analyze a simple thresholding algorithm which, outside of the narrow regime where the problem is hard, solves the associated mixed regression detection problem in $O(np)$ time with square-root the number of samples and matches the sample complexity required for (non-mixed) sparse linear regression; this allows the recovery problem to be subsequently solved by state-of-the-art techniques from the dense case. As a special case of our results, we show that this simple algorithm is order-optimal among a large family of algorithms in solving exact signed support recovery in sparse linear regression.

Complex diseases are caused by a multitude of factors that may differ between patients even within the same diagnostic category. A few underlying root causes may nevertheless initiate the development of disease within each patient. We therefore focus on identifying patient-specific root causes of disease, which we equate to the sample-specific predictivity of the exogenous error terms in a structural equation model. We generalize from the linear setting to the heteroscedastic noise model where $Y = m(X) + \varepsilon\sigma(X)$ with non-linear functions $m(X)$ and $\sigma(X)$ representing the conditional mean and mean absolute deviation, respectively. This model preserves identifiability but introduces non-trivial challenges that require a customized algorithm called Generalized Root Causal Inference (GRCI) to extract the error terms correctly. GRCI recovers patient-specific root causes more accurately than existing alternatives.

The paper uses structured machine learning regressions for nowcasting with panel data consisting of series sampled at different frequencies. Motivated by the problem of predicting corporate earnings for a large cross-section of firms with macroeconomic, financial, and news time series sampled at different frequencies, we focus on the sparse-group LASSO regularization which can take advantage of the mixed frequency time series panel data structures. Our empirical results show the superior performance of our machine learning panel data regression models over analysts' predictions, forecast combinations, firm-specific time series regression models, and standard machine learning methods.

Large language models (LLMs) have brought significant and transformative changes in human society. These models have demonstrated remarkable capabilities in natural language understanding and generation, leading to various advancements and impacts across several domains. We consider the in-context learning under two formulation for attention related regression in this work. Given matrices $A_1 \in \mathbb{R}^{n \times d}$, and $A_2 \in \mathbb{R}^{n \times d}$ and $B \in \mathbb{R}^{n \times n}$, the purpose is to solve some certain optimization problems: Normalized version $\min_{X} \| D(X)^{-1} \exp(A_1 X A_2^\top) - B \|_F^2$ and Rescaled version $\| \exp(A_1 X A_2^\top) - D(X) \cdot B \|_F^2$. Here $D(X) := \mathrm{diag}( \exp(A_1 X A_2^\top) {\bf 1}_n )$. Our regression problem shares similarities with previous studies on softmax-related regression. Prior research has extensively investigated regression techniques related to softmax regression: Normalized version $\| \langle \exp(Ax) , {\bf 1}_n \rangle^{-1} \exp(Ax) - b \|_2^2$ and Resscaled version $\| \exp(Ax) - \langle \exp(Ax), {\bf 1}_n \rangle b \|_2^2 $ In contrast to previous approaches, we adopt a vectorization technique to address the regression problem in matrix formulation. This approach expands the dimension from $d$ to $d^2$, resembling the formulation of the regression problem mentioned earlier. Upon completing the lipschitz analysis of our regression function, we have derived our main result concerning in-context learning.