Related papers: Continuation Methods for Mixing Heterogenous Sourc…

Homotopy optimization is a traditional method to deal with a complicated optimization problem by solving a sequence of easy-to-hard surrogate subproblems. However, this method can be very sensitive to the continuation schedule design and…

Researchers often have to deal with heterogeneous population with mixed regression relationships, increasingly so in the era of data explosion. In such problems, when there are many candidate predictors, it is not only of interest to…

In big data applications such as healthcare data mining, due to privacy concerns, it is necessary to collect predictions from multiple information sources for the same instance, with raw features being discarded or withheld when aggregating…

We aim to solve a topology optimization problem where the distribution of material in the design domain is represented by a density function. To obtain candidates for local minima, we want to solve the first order optimality system via…

We consider the optimal decision-making problem in a primary sample of interest with multiple auxiliary sources available. The outcome of interest is limited in the sense that it is only observed in the primary sample. In reality, such…

In the era of big data, the increasing availability of diverse data sources has driven interest in analytical approaches that integrate information across sources to enhance statistical accuracy, efficiency, and scientific insights. Many…

Homotopy methods are attractive due to their capability of solving difficult optimisation and optimal control problems. The underlying idea is to construct a homotopy, which may be considered as a continuous (zero) curve between the…

Combining complementary information from multiple modalities is intuitively appealing for improving the performance of learning-based approaches. However, it is challenging to fully leverage different modalities due to practical challenges…

Heterogeneous data from multiple populations, sub-groups, or sources is often represented as a ``mixture model'' with a single latent class influencing all of the observed covariates. Heterogeneity can be resolved at multiple levels by…

We introduce the concept of homotopy iterators for performing polynomial homotopy continuation tasks in a memory efficient manner. The main idea is to push forward an iterator for the start solutions of a homotopy via the function which…

Relational data sources are still one of the most popular ways to store enterprise or Web data, however, the issue with relational schema is the lack of a well-defined semantic description. A common ontology provides a way to represent the…

While automatically generated polynomial elimination templates have sparked great progress in the field of 3D computer vision, there remain many problems for which the degree of the constraints or the number of unknowns leads to…

Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing…

A method for solving zero-finding problems is developed by tracking homotopy paths, which define connecting channels between an auxiliary problem and the objective problem. Current algorithms' success highly relies on empirical knowledge,…

Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…

We use our recent implementation of a certified homotopy tracking algorithm to search for start systems that minimize the average complexity of finding all roots of a regular system of polynomial equations. While finding optimal start…

When trained on diverse labeled data, machine learning models have proven themselves to be a powerful tool in all facets of society. However, due to budget limitations, deliberate or non-deliberate censorship, and other problems during data…

Sample selection is a prevalent method in learning with noisy labels, where small-loss data are typically considered as correctly labeled data. However, this method may not effectively identify clean hard examples with large losses, which…

Partial multi-label learning and complementary multi-label learning are two popular weakly supervised multi-label classification paradigms that aim to alleviate the high annotation costs of collecting precisely annotated multi-label data.…

Modeling various aspects that make a music piece unique is a challenging task, requiring the combination of multiple sources of information. Deep learning is commonly used to obtain representations using various sources of information, such…