arXiv research

QRAFTI uses multi-agent framework to improve equity factor research.

We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. The first one satisfies MCP(0,3) and contains a subset isometric to $\mathbb{R}$, but does not topologically split. The second space satisfies…

We propose a minimax concave penalized multi-armed bandit algorithm under generalized linear model (G-MCP-Bandit) for a decision-maker facing high-dimensional data in an online learning and decision-making process. We demonstrate that the G-MCP-Bandit algorithm asymptotically achieves the optimal cumulative regret in t…

Perelman's doubling theorem asserts that the metric space obtained by gluing along their boundaries two copies of an Alexandrov space with curvature $\geq κ$ is an Alexandrov space with the same dimension and satisfying the same curvature lower bound. We show that this result cannot be extended to metric measure spaces…

Study Busemann spaces with measures under MCP, proving rigidity and structure theorems.

Proves rectifiability for specific metric spaces with unique tangents.

Measure contraction properties $MCP(K,N)$ are synthetic Ricci curvature lower bounds for metric measure spaces which do not necessarily have smooth structures. It is known that if a Riemannian manifold has dimension $N$, then $MCP(K,N)$ is equivalent to Ricci curvature bounded below by $K$. On the other hand, it was ob…

CD converges linearly for MCP/SCAD penalized least squares.

New sub-Riemannian structures fail synthetic curvature bounds.

Constructs Poisson structures on gauge orbits of Maurer-Cartan elements.

The paper examines curvature-dimension bounds on sub-Finsler Heisenberg groups.

We give necessary and sufficient conditions that show that both the group of isometries and the group of measure-preserving isometries are Lie groups for a large class of metric measure spaces. In addition we study, among other examples, whether spaces having a generalized lower Ricci curvature bound fulfill these requ…

Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has been proposed as a way of extending the ideas of the lasso to the problem of group…

Humans are able to perform a myriad of sophisticated tasks by drawing upon skills acquired through prior experience. For autonomous agents to have this capability, they must be able to extract reusable skills from past experience that can be recombined in new ways for subsequent tasks. Furthermore, when controlling com…

MCP extends conformal prediction to vector-valued score functions without data splitting.

Study improves keyword forecasting in earnings-call prediction markets.

In this paper, we prove that a metric measure space which has at least one open set isometric to an interval, and for which the (possibly non-unique) optimal transport map exists from any absolutely continuous measure to an arbitrary measure, is a one-dimensional manifold (possibly with boundary). As an immediate corol…

A new scheme for private computation splits client data into shares for server operations.

Assessing reliably the confidence of a deep neural network and predicting its failures is of primary importance for the practical deployment of these models. In this paper, we propose a new target criterion for model confidence, corresponding to the True Class Probability (TCP). We show how using the TCP is more suited…

To keep up with increasing dataset sizes and model complexity, distributed training has become a necessity for large machine learning tasks. Parameter servers ease the implementation of distributed parameter management---a key concern in distributed training---, but can induce severe communication overhead. To reduce c…

We prove that any corank 1 Carnot group of dimension $k+1$ equipped with a left-invariant measure satisfies the $\mathrm{MCP}(K,N)$ if and only if $K \leq 0$ and $N \geq k+3$. This generalizes the well known result by Juillet for the Heisenberg group $\mathbb{H}_{k+1}$ to a larger class of structures, which admit non-t…

Distributed gradient descent (DGD) is an efficient way of implementing gradient descent (GD), especially for large data sets, by dividing the computation tasks into smaller subtasks and assigning to different computing servers (CSs) to be executed in parallel. In standard parallel execution, per-iteration waiting time …

Algorithm stabilizes queues in asymmetric systems with unknown service rates.

One-bit measurements widely exist in the real world, and they can be used to recover sparse signals. This task is known as the problem of learning halfspaces in learning theory and one-bit compressive sensing (1bit-CS) in signal processing. In this paper, we propose novel algorithms based on both convex and nonconvex s…

Corella protects client data privacy in multi-server learning with correlated queries.

Federated learning has become increasingly important for modern machine learning, especially for data privacy-sensitive scenarios. Existing federated learning mostly adopts the central server-based architecture or centralized architecture. However, in many social network scenarios, centralized federated learning is not…

Machine Learning (ML) solutions are nowadays distributed and are prone to various types of component failures, which can be encompassed in so-called Byzantine behavior. This paper introduces LiuBei, a Byzantine-resilient ML algorithm that does not trust any individual component in the network (neither workers nor serve…

Study on curvature bounds and geodesic dimension in sub-Finsler Heisenberg groups.

Paper proposes sparse classification method for high-dimensional data.

New method speeds up distributed linear regression.

Study shows volume constraints lead to isoperimetric constant bounds in specific metric spaces.

Paper explores differential privacy in high-dimensional federated learning, tackling server trustworthiness and estimation.

This paper makes two contributions to Bayesian machine learning algorithms. Firstly, we propose stochastic natural gradient expectation propagation (SNEP), a novel alternative to expectation propagation (EP), a popular variational inference algorithm. SNEP is a black box variational algorithm, in that it does not requi…

Federated learning obtains a central model on the server by aggregating models trained locally on clients. As a result, federated learning does not require clients to upload their data to the server, thereby preserving the data privacy of the clients. One challenge in federated learning is to reduce the client-server c…

CSE-FSL reduces communication and storage costs in federated learning.

Measure contraction property is a synthetic Ricci curvature lower bound for metric measure spaces. We consider Sasakian manifolds with non-negative Tanaka-Webster Ricci curvature equipped with the metric measure space structure defined by the sub-Riemannian metric and the Popp measure. We show that these spaces satisfy…

Machine Learning (ML) solutions are nowadays distributed, according to the so-called server/worker architecture. One server holds the model parameters while several workers train the model. Clearly, such architecture is prone to various types of component failures, which can be all encompassed within the spectrum of a …

New method reduces FL communication cost by leveraging server's side information.

Communication on heterogeneous edge networks is a fundamental bottleneck in Federated Learning (FL), restricting both model capacity and user participation. To address this issue, we introduce two novel strategies to reduce communication costs: (1) the use of lossy compression on the global model sent server-to-client;…

Detects backdoors in outsourced models by replicating training steps across multiple servers.

This paper improves privacy in federated learning without a trusted server.

This work provides bounds on generalization error and privacy leakage in federated learning.

Paper tackles federated linear bandit learning with AirComp for noisy channels.

DFedAvgM is a decentralized FedAvg with momentum for privacy and communication efficiency.

Paper proposes a GPU-based system for training massive deep learning models in ads systems.

Paper improves communication in distributed optimization, reducing worker-to-server data exchanges.

We propose three new robust aggregation rules for distributed synchronous Stochastic Gradient Descent~(SGD) under a general Byzantine failure model. The attackers can arbitrarily manipulate the data transferred between the servers and the workers in the parameter server~(PS) architecture. We prove the Byzantine resilie…

This paper proposes a cooperative mechanism for mitigating the performance degradation due to non-independent-and-identically-distributed (non-IID) data in collaborative machine learning (ML), namely federated learning (FL), which trains an ML model using the rich data and computational resources of mobile clients with…