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Harm Derksen

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

4 papers

2 author rows

FOCS Conference 2024 Conference Paper

Boosting Uniformity in Quasirandom Groups: Fast and Simple

Harm Derksen
Chin Ho Lee
Emanuele Viola

We study the communication complexity of multiplying $k\times t$ elements from the group $H$ = SL $(2, q)$ in the number-on-forehead model with $k$ parties. We prove a lower bound of $(t\log H)/c^{k}$. This is an exponential improvement over previous work, and matches the state-of-the-art in the area. Relatedly, we show that the convolution of $k^{c}$ independent copies of a 3-uniform distribution over $H^{m}$ is close to a $k$ - uniform distribution. This is again an exponential improvement over previous work which needed $c^{k}$ copies. The proofs are remarkably simple; the results extend to other quasirandom groups. We also show that for any group $LI$, any distribution over $H^{m}$ whose weight-k Fourier coefficients are small is close to a k-uniform distribution. This generalizes previous work in the abelian setting, and the proof is simpler.

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JBHI Journal 2023 Journal Article

A Novel Tropical Geometry-Based Interpretable Machine Learning Method: Pilot Application to Delivery of Advanced Heart Failure Therapies

Heming Yao
Harm Derksen
Jessica R. Golbus
Justin Zhang
Keith D. Aaronson
Jonathan Gryak
Kayvan Najarian

A model's interpretability is essential to many practical applications such as clinical decision support systems. In this article, a novel interpretable machine learning method is presented, which can model the relationship between input variables and responses in humanly understandable rules. The method is built by applying tropical geometry to fuzzy inference systems, wherein variable encoding functions and salient rules can be discovered by supervised learning. Experiments using synthetic datasets were conducted to demonstrate the performance and capacity of the proposed algorithm in classification and rule discovery. Furthermore, we present a pilot application in identifying heart failure patients that are eligible for advanced therapies as proof of principle. From our results on this particular application, the proposed network achieves the highest F1 score. The network is capable of learning rules that can be interpreted and used by clinical providers. In addition, existing fuzzy domain knowledge can be easily transferred into the network and facilitate model training. In our application, with the existing knowledge, the F1 score was improved by over 5%. The characteristics of the proposed network make it promising in applications requiring model reliability and justification.

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FOCS Conference 2022 Conference Paper

Fooling polynomials using invariant theory *

Harm Derksen
Emanuele Viola

We revisit the problem of constructing explicit pseudorandom generators that fool with error ϵ degree-d polynomials in n variables over the field F q, in the case of large q. Previous constructions either have seed length $\geq 2^{d}\log q$, and thus are only non-trivial when $d\lt \log n$, or else rely on a seminal reduction by Bogdanov (STOC 2005). This reduction yields seed length not less than $d^{4}\log n+\log q$ and requires fields of size $q\geq d^{6}/\epsilon^{2}$; and explicit generators meeting such bounds are known. Departing from Bogdanov’s reduction, we develop an algebraic analogue of the Bogdanov-Viola paradigm (FOCS 2007, SICOMP 2010) of summing generators for degree-one polynomials. Whereas previous analyses of the paradigm are restricted to degree $d\lt \log n$, we give a new analysis which handles large degrees. A main new idea is to show that the construction preserves indecomposability of polynomials. Apparently for the first time in the area, the proof uses invariant theory. Our approach in particular yields several new pseudorandom generators. In particular, for large enough fields we obtain seed length $O(d\log n+\log q)$ which is optimal up to constant factors. We also construct generators for fields of size as small as $O(d^{4})$. Further reducing the field size requires a significant change in techniques: Most or all generators for large-degree polynomials rely on Weil bounds; but such bounds are only applicable when $q\gt d^{4}$

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AIIM Journal 2021 Journal Article

Multimodal tensor-based method for integrative and continuous patient monitoring during postoperative cardiac care

Larry Hernandez
Renaid Kim
Neriman Tokcan
Harm Derksen
Ben E. Biesterveld
Alfred Croteau
Aaron M. Williams
Michael Mathis

Patients recovering from cardiovascular surgeries may develop life-threatening complications such as hemodynamic decompensation, making the monitoring of patients for such complications an essential component of postoperative care. However, this need has given rise to an inexorable increase in the number and modalities of data points collected, making it challenging to effectively analyze in real time. While many algorithms exist to assist in monitoring these patients, they often lack accuracy and specificity, leading to alarm fatigue among healthcare practitioners. In this study we propose a multimodal approach that incorporates salient physiological signals and EHR data to predict the onset of hemodynamic decompensation. A retrospective dataset of patients recovering from cardiac surgery was created and used to train predictive models. Advanced signal processing techniques were employed to extract complex features from physiological waveforms, while a novel tensor-based dimensionality reduction method was used to reduce the size of the feature space. These methods were evaluated for predicting the onset of decompensation at varying time intervals, ranging from a half-hour to 12 h prior to a decompensation event. The best performing models achieved AUCs of 0. 87 and 0. 80 for the half-hour and 12-h intervals respectively. These analyses evince that a multimodal approach can be used to develop clinical decision support systems that predict adverse events several hours in advance.

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