To alleviate the shortage of computing power faced by clients in training deep neural networks (DNNs) using federated learning (FL), we leverage the edge computing and split learning to propose a model-splitting allowed FL (SFL) framework, with the aim to minimize the training latency without loss of test accuracy. Under the synchronized global update setting, the latency to complete a round of global training is determined by the maximum latency for the clients to complete a local training session. Therefore, the training latency minimization problem (TLMP) is modelled as a minimizing-maximum problem. To solve this mixed integer nonlinear programming problem, we first propose a regression method to fit the quantitative-relationship between the cut-layer and other parameters of an AI-model, and thus, transform the TLMP into a continuous problem. Considering that the two subproblems involved in the TLMP, namely, the cut-layer selection problem for the clients and the computing resource allocation problem for the parameter-server are relative independence, an alternate-optimization-based algorithm with polynomial time complexity is developed to obtain a high-quality solution to the TLMP. Extensive experiments are performed on a popular DNN-model EfficientNetV2 using dataset MNIST, and the results verify the validity and improved performance of the proposed SFL framework.

In the era of data-driven science, machine learning has emerged as a transformative tool, offering unprecedented solutions to complex problems across a wide range of scientific and technological domains. Specifically, machine learning has found applications in diverse fields such as biology, medicine, material science, engineering, energy, manufacturing, and agriculture. Notable examples include rapid detection of SARS-CoV-2 Ikponmwoba et al. [2022], advances in drug discovery and development Talevi et al. [2020], quality control and defect detection Wang et al. [2022], climate modeling and prediction Krasnopolsky and Fox-Rabinovitz [2006], as well as crop yield forecasting and optimization Di et al. [2022]. Some of these applications involve classification, which involves learning based on categorical data. In this regard, machine learning techniques, such as Support Vector Machines, Naive Bayes, K-nearest neighbor, and Neural Networks, have been used to extract texture features from images for subsequent classification Chola et al. [2022a,b]. Additionally, machine learning has facilitated the identification of high-order closure terms from fully kinetic simulations, a critical aspect of multi-scale modelingLaperre et al. [2022]. On the other hand, function approximation or regression involves estimating a continuous target quantity as a function of a set of input variables. Methods such as Sparse Identification of Nonlinear Dynamics (SINDy) Brunton et al. [2016], the Least Absolute Shrinkage and Selection Operator (LASSO) Tibshirani [1996], Dynamic Mode Decomposition (DMD) Schmid [2010], Mezić [2005], Koopman operator Mezić [2013] and the Eigensystem Realization Algorithm (ERA) Juang and Pappa [1985] have contributed significantly to understanding complex systems by offering effective strategies for model selection, variable regularization, decomposition of high-dimensional systems, and extraction of state-space models from input-output data.

In this paper, we find and analyze that we can easily drop the double descent by only adding one dropout layer before the fully-connected linear layer. The surprising double-descent phenomenon has drawn public attention in recent years, making the prediction error rise and drop as we increase either sample or model size. The current paper shows that it is possible to alleviate these phenomena by using optimal dropout in the linear regression model and the nonlinear random feature regression, both theoretically and empirically. % ${y}=X{\beta}^0+{\epsilon}$ with $X\in\mathbb{R}^{n\times p}$. We obtain the optimal dropout hyperparameter by estimating the ground truth ${\beta}^0$ with generalized ridge typed estimator $\hat{{\beta}}=(X^TX+\alpha\cdot\mathrm{diag}(X^TX))^{-1}X^T{y}$. Moreover, we empirically show that optimal dropout can achieve a monotonic test error curve in nonlinear neural networks using Fashion-MNIST and CIFAR-10. Our results suggest considering dropout for risk curve scaling when meeting the peak phenomenon. In addition, we figure out why previous deep learning models do not encounter double-descent scenarios -- because we already apply a usual regularization approach like the dropout in our models. To our best knowledge, this paper is the first to analyze the relationship between dropout and double descent.

We formalize the problem of machine unlearning as design of efficient unlearning algorithms corresponding to learning algorithms which perform a selection of adaptive queries from structured query classes. We give efficient unlearning algorithms for linear and prefix-sum query classes. As applications, we show that unlearning in many problems, in particular, stochastic convex optimization (SCO), can be reduced to the above, yielding improved guarantees for the problem. In particular, for smooth Lipschitz losses and any $\rho>0$, our results yield an unlearning algorithm with excess population risk of $\tilde O\big(\frac{1}{\sqrt{n}}+\frac{\sqrt{d}}{n\rho}\big)$ with unlearning query (gradient) complexity $\tilde O(\rho \cdot \text{Retraining Complexity})$, where $d$ is the model dimensionality and $n$ is the initial number of samples. For non-smooth Lipschitz losses, we give an unlearning algorithm with excess population risk $\tilde O\big(\frac{1}{\sqrt{n}}+\big(\frac{\sqrt{d}}{n\rho}\big)^{1/2}\big)$ with the same unlearning query (gradient) complexity. Furthermore, in the special case of Generalized Linear Models (GLMs), such as those in linear and logistic regression, we get dimension-independent rates of $\tilde O\big(\frac{1}{\sqrt{n}} +\frac{1}{(n\rho)^{2/3}}\big)$ and $\tilde O\big(\frac{1}{\sqrt{n}} +\frac{1}{(n\rho)^{1/3}}\big)$ for smooth Lipschitz and non-smooth Lipschitz losses respectively. Finally, we give generalizations of the above from one unlearning request to \textit{dynamic} streams consisting of insertions and deletions.

The prediction of spin magnitudes in binary black hole and neutron star mergers is crucial for understanding the astrophysical processes and gravitational wave (GW) signals emitted during these cataclysmic events. In this paper, we present a novel Neuro-Symbolic Architecture (NSA) that combines the power of neural networks and symbolic regression to accurately predict spin magnitudes of black hole and neutron star mergers. Our approach utilizes GW waveform data obtained from numerical relativity simulations in the SXS Waveform catalog. By combining these two approaches, we leverage the strengths of both paradigms, enabling a comprehensive and accurate prediction of spin magnitudes. Our experiments demonstrate that the proposed architecture achieves an impressive root-mean-squared-error (RMSE) of 0.05 and mean-squared-error (MSE) of 0.03 for the NSA model and an RMSE of 0.12 for the symbolic regression model alone. We train this model to handle higher-order multipole waveforms, with a specific focus on eccentric candidates, which are known to exhibit unique characteristics. Our results provide a robust and interpretable framework for predicting spin magnitudes in mergers. This has implications for understanding the astrophysical properties of black holes and deciphering the physics underlying the GW signals.

A very popular model-agnostic technique for explaining predictive models is the SHapley Additive exPlanation (SHAP). The two most popular versions of SHAP are a conditional expectation version and an unconditional expectation version (the latter is also known as interventional SHAP). Except for tree-based methods, usually the unconditional version is used (for computational reasons). We provide a (surrogate) neural network approach which allows us to efficiently calculate the conditional version for both neural networks and other regression models, and which properly considers the dependence structure in the feature components. This proposal is also useful to provide drop1 and anova analyses in complex regression models which are similar to their generalized linear model (GLM) counterparts, and we provide a partial dependence plot (PDP) counterpart that considers the right dependence structure in the feature components.

Foundation large language models (LLMs) have shown an impressive ability to solve tasks across a wide range of fields including health. To effectively solve personalized health tasks, LLMs need the ability to ingest a diversity of data modalities that are relevant to an individual's health status. In this paper, we take a step towards creating multimodal LLMs for health that are grounded in individual-specific data by developing a framework (HeLM: Health Large Language Model for Multimodal Understanding) that enables LLMs to use high-dimensional clinical modalities to estimate underlying disease risk. HeLM encodes complex data modalities by learning an encoder that maps them into the LLM's token embedding space and for simple modalities like tabular data by serializing the data into text. Using data from the UK Biobank, we show that HeLM can effectively use demographic and clinical features in addition to high-dimensional time-series data to estimate disease risk. For example, HeLM achieves an AUROC of 0.75 for asthma prediction when combining tabular and spirogram data modalities compared with 0.49 when only using tabular data. Overall, we find that HeLM outperforms or performs at parity with classical machine learning approaches across a selection of eight binary traits. Furthermore, we investigate the downstream uses of this model such as its generalizability to out-of-distribution traits and its ability to power conversations around individual health and wellness.

Quantum computing has the potential to provide substantial computational advantages over current state-of-the-art classical supercomputers. However, current hardware is not advanced enough to execute fault-tolerant quantum algorithms. An alternative of using hybrid quantum-classical computing with variational algorithms can exhibit barren plateau issues, causing slow convergence of gradient-based optimization techniques. In this paper, we discuss "post-variational strategies", which shift tunable parameters from the quantum computer to the classical computer, opting for ensemble strategies when optimizing quantum models. We discuss various strategies and design principles for constructing individual quantum circuits, where the resulting ensembles can be optimized with convex programming. Further, we discuss architectural designs of post-variational quantum neural networks and analyze the propagation of estimation errors throughout such neural networks. Lastly, we show that our algorithm can be applied to real-world applications such as image classification on handwritten digits, producing a 96% classification accuracy.

Our motivation is to shed light the performance of the widely popular "R-Learner." Like many other methods for estimating conditional average treatment effects (CATEs), R-Learning can be expressed as a weighted pseudo-outcome regression (POR). Previous comparisons of POR techniques have paid careful attention to the choice of pseudo-outcome transformation. However, we argue that the dominant driver of performance is actually the choice of weights. Specifically, we argue that R-Learning implicitly performs an inverse-variance weighted form of POR. These weights stabilize the regression and allow for convenient simplifications of bias terms.

We consider the problem of learning a sparse graph underlying an undirected Gaussian graphical model, a key problem in statistical machine learning. Given $n$ samples from a multivariate Gaussian distribution with $p$ variables, the goal is to estimate the $p \times p$ inverse covariance matrix (aka precision matrix), assuming it is sparse (i.e., has a few nonzero entries). We propose GraphL0BnB, a new estimator based on an $\ell_0$-penalized version of the pseudolikelihood function, while most earlier approaches are based on the $\ell_1$-relaxation. Our estimator can be formulated as a convex mixed integer program (MIP) which can be difficult to compute at scale using off-the-shelf commercial solvers. To solve the MIP, we propose a custom nonlinear branch-and-bound (BnB) framework that solves node relaxations with tailored first-order methods. As a by-product of our BnB framework, we propose large-scale solvers for obtaining good primal solutions that are of independent interest. We derive novel statistical guarantees (estimation and variable selection) for our estimator and discuss how our approach improves upon existing estimators. Our numerical experiments on real/synthetic datasets suggest that our method can solve, to near-optimality, problem instances with $p = 10^4$ -- corresponding to a symmetric matrix of size $p \times p$ with $p^2/2$ binary variables. We demonstrate the usefulness of GraphL0BnB versus various state-of-the-art approaches on a range of datasets.