We present a nonparametric interpretation for deep learning compatible modern Hopfield models and utilize this new perspective to debut efficient variants. Our key contribution stems from interpreting the memory storage and retrieval processes in modern Hopfield models as a nonparametric regression problem subject to a set of query-memory pairs. Interestingly, our framework not only recovers the known results from the original dense modern Hopfield model but also fills the void in the literature regarding efficient modern Hopfield models, by introducing sparse-structured modern Hopfield models with sub-quadratic complexity. We establish that this sparse model inherits the appealing theoretical properties of its dense analogue — connection with transformer attention, fixed point convergence and exponential memory capacity. Additionally, we showcase the versatility of our framework by constructing a family of modern Hopfield models as extensions, including linear, random masked, top-$K$ and positive random feature modern Hopfield models. Empirically, we validate our framework in both synthetic and realistic settings for memory retrieval and learning tasks.

SUMMARY: Spatial transcriptomics (ST) allows gene expression profiling within intact tissue samples but lacks single-cell resolution. This necessitates computational deconvolution methods to estimate the contributions of distinct cell types. This article introduces NLSDeconv, a novel cell-type deconvolution method based on non-negative least squares, along with an accompanying Python package. Benchmarking against 18 existing deconvolution methods on various ST datasets demonstrates NLSDeconv's competitive statistical performance and superior computational efficiency. AVAILABILITY AND IMPLEMENTATION: NLSDeconv is freely available at https://github.com/tinachentc/NLSDeconv as a Python package.

We consider the problem of instance-optimal statistical estimation under the constraint of differential privacy where mechanisms must adapt to the difficulty of the input dataset. We prove a new instance specific lower bound using a new divergence and show it characterizes the local minimax optimal rates for private statistical estimation. We propose two new mechanisms that are universally instance-optimal for general estimation problems up to logarithmic factors. Our first mechanism, the total variation mechanism, builds on the exponential mechanism with stable approximations of the total variation distance, and is universally instance-optimal in the high privacy regime $\epsilon \leq 1/\sqrt{n}$. Our second mechanism, the T-mechanism, is based on the T-estimator framework (Birg{é}, 2006) using the clipped log likelihood ratio as a stable test: it attains instance-optimal rates for any $\epsilon \leq 1$ up to logarithmic factors. Finally, we study the implications of our results to robust statistical estimation, and show that our algorithms are universally optimal for this problem, characterizing the optimal minimax rates for robust statistical estimation.

We provide a general constrained risk inequality that applies to arbitrary non-decreasing losses, extending a result of Brown and Low [\emph{Ann. Stat. 1996}]. Given two distributions $P_0$ and $P_1$, we find a lower bound for the risk of estimating a parameter $\theta(P_1)$ under $P_1$ given an upper bound on the risk of estimating the parameter $\theta(P_0)$ under $P_0$. The inequality is a useful pedagogical tool, as its proof relies only on the Cauchy-Schwartz inequality, it applies to general losses, and it transparently gives risk lower bounds on super-efficient and adaptive estimators.

Much work has been done recently to make neural networks more interpretable, and one approach is to arrange for the network to use only a subset of the available features. In linear models, Lasso (or $\ell_1$-regularized) regression assigns zero weights to the most irrelevant or redundant features, and is widely used in data science. However the Lasso only applies to linear models. Here we introduce LassoNet, a neural network framework with global feature selection. Our approach achieves feature sparsity by allowing a feature to participate in a hidden unit only if its linear representative is active. Unlike other approaches to feature selection for neural nets, our method uses a modified objective function with constraints, and so integrates feature selection with the parameter learning directly. As a result, it delivers an entire regularization path of solutions with a range of feature sparsity. In experiments with real and simulated data, LassoNet significantly outperforms state-of-the-art methods for feature selection and regression. The LassoNet method uses projected proximal gradient descent, and generalizes directly to deep networks. It can be implemented by adding just a few lines of code to a standard neural network.

Much work has been done recently to make neural networks more interpretable, and one approach is to arrange for the network to use only a subset of the available features. In linear models, Lasso (or $\ell_1$-regularized) regression assigns zero weights to the most irrelevant or redundant features, and is widely used in data science. However the Lasso only applies to linear models. Here we introduce LassoNet, a neural network framework with global feature selection. Our approach achieves feature sparsity by adding a skip (residual) layer and allowing a feature to participate in any hidden layer only if its skip-layer representative is active. Unlike other approaches to feature selection for neural nets, our method uses a modified objective function with constraints, and so integrates feature selection with the parameter learning directly. As a result, it delivers an entire regularization path of solutions with a range of feature sparsity. We apply LassoNet to a number of real-data problems and find that it significantly outperforms state-of-the-art methods for feature selection and regression. LassoNet uses projected proximal gradient descent, and generalizes directly to deep networks. It can be implemented by adding just a few lines of code to a standard neural network.

We study two-sided matching markets in which one side of the market (the players) does not have a priori knowledge about its preferences for the other side (the arms) and is required to learn its preferences from experience. Also, we assume the players have no direct means of communication. This model extends the standard stochastic multi-armed bandit framework to a decentralized multiple player setting with competition. We introduce a new algorithm for this setting that, over a time horizon $T$, attains $\mathcal{O}(\log(T))$ stable regret when preferences of the arms over players are shared, and $\mathcal{O}(\log(T)^2)$ regret when there are no assumptions on the preferences on either side. Moreover, in the setting where a single player may deviate, we show that the algorithm is incentive-compatible whenever the arms' preferences are shared, but not necessarily so when preferences are fully general.

We study the stochastic batched convex optimization problem, in which we use many \emph{parallel} observations to optimize a convex function given limited rounds of interaction. In each of $M$ rounds, an algorithm may query for information at $n$ points, and after issuing all $n$ queries, it receives unbiased noisy function and/or (sub)gradient evaluations at the $n$ points. After $M$ such rounds, the algorithm must output an estimator. We provide lower and upper bounds on the performance of such batched convex optimization algorithms in zeroth and first-order settings for Lipschitz convex and smooth strongly convex functions. Our rates of convergence (nearly) achieve the fully sequential rate once $M = O(d \log \log n)$, where $d$ is the problem dimension, but the rates may exponentially degrade as the dimension $d$ increases, in distinction from fully sequential settings.

Nowadays, a large number of groups choose to deploy their applications to cloud platforms, especially for the big data era. Currently, the hybrid cloud is one of the most popular computing paradigms for holding the privacy-aware applications driven by the requirements of privacy protection and cost saving. However, it is still a challenge to realize data placement considering both the energy consumption in private cloud and the cost for renting the public cloud services. In view of this challenge, a cost and energy aware data placement method, named CEDP, for privacy-aware applications over big data in hybrid cloud is proposed. Technically, formalized analysis of cost, access time, and energy consumption is conducted in the hybrid cloud environment. Then a corresponding data placement method is designed to accomplish the cost saving for renting the public cloud services and energy savings for task execution within the private cloud platforms. Experimental evaluations validate the efficiency and effectiveness of our proposed method.