اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدLearning Lines with Ordinal Constraints
91
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the problem of finding a mapping $f$ from a set of points into the real line, under ordinal triple constraints. An ordinal constraint for a triple of points $(u,v,w)$ asserts that $|f(u)-f(v)|<|f(u)-f(w)|$. We present an approximation algorithm for the dense case of this problem. Given an instance that admits a solution that satisfies $(1-varepsilon)$-fraction of all constraints, our algorithm computes a solution that satisfies $(1-O(varepsilon^{1/8}))$-fraction of all constraints, in time $O(n^7) + (1/varepsilon)^{O(1/varepsilon^{1/8})} n$.
قيم البحث
اقرأ أيضاً
Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric $A$ as $L
^TL$, the problem can be cast as looking for a linear map between two sets of points in different spaces, meanwhile maintaining some data structures. The ordinal relation of the labels can be maintained via classical multidimensional scaling, a popular tool for dimension reduction in statistics. A least squares fitting term is then introduced to the cost function, which can also maintain the local data structure. The resulting model is an unconstrained problem, and can better fit the data structure. Extensive numerical results demonstrate the improvement of the new approach over the linear distance metric learning model both in speed and ranking performance.
Polynomial regression is a basic primitive in learning and statistics. In its most basic form the goal is to fit a degree $d$ polynomial to a response variable $y$ in terms of an $n$-dimensional input vector $x$. This is extremely well-studied with m
any applications and has sample and runtime complexity $Theta(n^d)$. Can one achieve better runtime if the intrinsic dimension of the data is much smaller than the ambient dimension $n$? Concretely, we are given samples $(x,y)$ where $y$ is a degree at most $d$ polynomial in an unknown $r$-dimensional projection (the relevant dimensions) of $x$. This can be seen both as a generalization of phase retrieval and as a special case of learning multi-index models where the link function is an unknown low-degree polynomial. Note that without distributional assumptions, this is at least as hard as junta learning. In this work we consider the important case where the covariates are Gaussian. We give an algorithm that learns the polynomial within accuracy $epsilon$ with sample complexity that is roughly $N = O_{r,d}(n log^2(1/epsilon) (log n)^d)$ and runtime $O_{r,d}(N n^2)$. Prior to our work, no such results were known even for the case of $r=1$. We introduce a new filtered PCA approach to get a warm start for the true subspace and use geodesic SGD to boost to arbitrary accuracy; our techniques may be of independent interest, especially for problems dealing with subspace recovery or analyzing SGD on manifolds.
Distributed machine learning (ML) at network edge is a promising paradigm that can preserve both network bandwidth and privacy of data providers. However, heterogeneous and limited computation and communication resources on edge servers (or edges) po
se great challenges on distributed ML and formulate a new paradigm of Edge Learning (i.e. edge-cloud collaborative machine learning). In this article, we propose a novel framework of learning to learn for effective Edge Learning (EL) on heterogeneous edges with resource constraints. We first model the dynamic determination of collaboration strategy (i.e. the allocation of local iterations at edge servers and global aggregations on the Cloud during collaborative learning process) as an online optimization problem to achieve the tradeoff between the performance of EL and the resource consumption of edge servers. Then, we propose an Online Learning for EL (OL4EL) framework based on the budget-limited multi-armed bandit model. OL4EL supports both synchronous and asynchronous learning patterns, and can be used for both supervised and unsupervised learning tasks. To evaluate the performance of OL4EL, we conducted both real-world testbed experiments and extensive simulations based on docker containers, where both Support Vector Machine and K-means were considered as use cases. Experimental results demonstrate that OL4EL significantly outperforms state-of-the-art EL and other collaborative ML approaches in terms of the trade-off between learning performance and resource consumption.
Uncertainty is the only certainty there is. Modeling data uncertainty is essential for regression, especially in unconstrained settings. Traditionally the direct regression formulation is considered and the uncertainty is modeled by modifying the out
put space to a certain family of probabilistic distributions. On the other hand, classification based regression and ranking based solutions are more popular in practice while the direct regression methods suffer from the limited performance. How to model the uncertainty within the present-day technologies for regression remains an open issue. In this paper, we propose to learn probabilistic ordinal embeddings which represent each data as a multivariate Gaussian distribution rather than a deterministic point in the latent space. An ordinal distribution constraint is proposed to exploit the ordinal nature of regression. Our probabilistic ordinal embeddings can be integrated into popular regression approaches and empower them with the ability of uncertainty estimation. Experimental results show that our approach achieves competitive performance. Code is available at https://github.com/Li-Wanhua/POEs.
We study the problem of learning the causal relationships between a set of observed variables in the presence of latents, while minimizing the cost of interventions on the observed variables. We assume access to an undirected graph $G$ on the observe
d variables whose edges represent either all direct causal relationships or, less restrictively, a superset of causal relationships (identified, e.g., via conditional independence tests or a domain expert). Our goal is to recover the directions of all causal or ancestral relations in $G$, via a minimum cost set of interventions. It is known that constructing an exact minimum cost intervention set for an arbitrary graph $G$ is NP-hard. We further argue that, conditioned on the hardness of approximate graph coloring, no polynomial time algorithm can achieve an approximation factor better than $Theta(log n)$, where $n$ is the number of observed variables in $G$. To overcome this limitation, we introduce a bi-criteria approximation goal that lets us recover the directions of all but $epsilon n^2$ edges in $G$, for some specified error parameter $epsilon > 0$. Under this relaxed goal, we give polynomial time algorithms that achieve intervention cost within a small constant factor of the optimal. Our algorithms combine work on efficient intervention design and the design of low-cost separating set systems, with ideas from the literature on graph property testing.
الأسئلة المقترحة
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
