Date/Time : 25 Sep 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Hsuan-Tien Lin, National Taiwan University

Complementary-Label Learning (CLL) is a weakly supervised learning paradigm that is claimed to be useful in situations where collecting true labels is expensive. This talk begins by walking the audience through two advances in CLL. The first work discovered that the CLL loss design from Unbiased Risk Estimator (URE) suffers from high variance in gradient estimation. To address this, a novel surrogate complementary loss (SCL) framework is proposed, which reduces variance and improves gradient alignment, mitigating the overfitting issue. The second work introduces a new approach to CLL by reducing the problem to estimating the probability of complementary classes. This framework sidesteps the limitations of traditional methods and improves robustness in noisy environments, offering a broader perspective for both deep and non-deep models. Empirical results demonstrate the efficacy of both approaches in improving CLL performance. Finally, the speaker will share some of the ongoing attempts in making CLL more realistic, including some first-hand experience in collecting real-world datasets and releasing an open-source library.

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Date/Time : 09 Sep 2024 16:00
Venue : S17 #05-11 (SR5)
Speaker : Jean-Bernard Lasserre, LAAS-CNRS

We briefly describe the Christoffel-Darboux (CD) kernel and the Christoffel function (CF). While well-known tools in orthogonal polynomials and approximation theory, it is only recently that CF’s properties have been shown to be very useful and powerful (as well as easy to implement) to help solve some problems

— in data analysis and datra mining where the underlying (empirical) measure is usually discrete, e.g. for outlier detection, support inference, density approximation, and

— in approximation of discontinuous functions.

Finally we will also briefly describe some (in the author’s opinion surprising) links of the CF with seemingly less disconnected areas (Pell equation, equilibrium measure, convex optimization and positivity certificates).

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Date/Time : 23 Aug 2024 10:00
Venue : S17 #06-11 (SR6)
Speaker : Yixuan Wang, Caltech

We drew inspiration from the Kolmogorov–Arnold representation theory, using a composition of sum of 1D functions to represent higher dimensional functions, and proposed KANs, which has learnable activation functions parameterized by splines. Compared with MLPs, it will have much better scaling laws and interpretability since we use a much smaller network with 1D functions, provided that the underlying function has such a smooth representation, and in practice we can make KANs arbitrarily wide and deep. We demonstrate the wide applicability of this paradigm by examples of function pitting, PDE solving (PINNs), and applications to scientific problems. I will also discuss the most up-to-date developments of KANs and present some theoretical understandings.

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Date/Time : 30 Jul 2024 15:00
Venue : S17 #04-05 (SR2)
Speaker : Min XU, Carnegie Mellon University

Cryo-electron tomography (cryo-ET) 3D imaging technology captures a 3D image of a single cell’s subcellular structures at sub-molecular resolution and in a near-native state. It provides unprecedented opportunities for systematically studying the native spatial organization of subcellular structures, especially macromolecules. However, cryo-ET has high structural complexity and imaging limits, such as high structural diversity and crowding, low signal-to-noise ratio, and missing values. These have made the automated systematic analysis of such images extremely difficult. I will present our recent efforts to develop methods for automated analysis of cryo-ET data.

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Date/Time : 19 Jun 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Yuan Yancheng, Hong Kong Polytechnic University

Convex clustering model has attracted growing attention in the machine learning community. In this talk, we will introduce some recent progress of convex clustering model on model performance and numerical computation. Moreover, we will introduce a newly developed solver for solving the convex clustering model with GPU acceleration.  

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Date/Time : 18 Jun 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Weng Kee Wong, University of California at Los Angeles

This talk first reviews mathematical techniques for constructing various types of optimal experimental designs before I present applications to design early phase clinical trials. For more complex problems, the methodology is increasingly combined with nature-inspired metaheuristics, which are assumptions free, general-purpose optimization algorithms motivated by nature, like animal behavior. After a quick overview of metaheuristics, I use MATLAB and demonstrate how these algorithms can efficiently find multiple-objective optimal designs for a biomedical problem. E-optimal designs are a minimax type of optimal designs that pose particular mathematical challenges and I discuss some of them, including a continuing effort to find a practically useful algorithm for generating E-optimal designs and has a proof of convergence.

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Date/Time : 29 May 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Renbo Zhao, University of Iowa

We present and analyze a new Frank–Wolfe method for minimizing a -log-homogenous self-concordant barriers, with applications including positron emission tomography, D-optimal design, TV-regularized Poisson image de-blurring, quantum state tomography. The iteration complexity of our method is essentially , which recovers that obtained by Khachiyan (1996) on the D-optimal design problem. In addition, we also present and analyze an away-step variant of our proposed Frank–Wolfe method, and we show the global linear convergence of this method. When specialized to the D-optimal design problem, this settles an open problem in Ahipasaoglu, Sun and Todd (2008).

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Date/Time : 06 Mar 2024 15:00
Venue : S17 #05-12 (SR4)
Speaker : Akiko Takeda, University of Tokyo

Random projection techniques based on the Johnson-Lindenstrauss lemma are used for randomly aggregating the constraints or variables of optimization problems while approximately preserving their optimal values, which leads to smaller-scale optimization problems. In this talk, we show a few applications of random matrix techniques for constructing random subspace algorithms that iteratively solve smaller-scale subproblems and discuss their convergence speed. This talk is based on joint works with Ryota Nozawa, and Pierre-Louis Poirion.

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Date/Time : 06 Mar 2024 15:40
Venue : S17 #05-12 (SR4)
Speaker : Pierre-Louis Poirion, University of Tokyo

In this talk, we present a randomized subspace regularized Newton method for a non-convex function. We show that our method has global convergence under appropriate assumptions, and its convergence rate is the same as that of the full regularized Newton method. Furthermore, we can obtain a local linear convergence rate, under some additional assumptions, and prove that this rate is the best we can hope, under local strong convexity sumptions, when using random subspace. Finally, we will prove that under rank deficiency conditions, one can obtain super-linear convergence in the subspace setting.

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