arXiv subjects

Sankeerth Rao Karingula

Publications and source records attributed to Sankeerth Rao Karingula.

6 recordsLinked to original sources

arXiv2026

A simplified proof of polynomial improvements for 3SUM and APSP

We give a simplified proof of the polynomial improvements for integer 3SUM and all-pairs shortest paths (APSP) established by Alman and Vassilevska Williams, with weaker exponents. The central ingredient is selected-entry matrix multiplication: computing a prescribed set of entries of a product of dense rectangular matrices. Starting from Schönhage's inner/outer-product identity, we construct a multiplication rule that shares intermediate products among many outputs. We apply this rule recursively and bound the work by counting the requested entries at each level. Applied to incidence matrices, the algorithm solves Offline Set Disjointness over a small universe. Known deterministic reductions then yield truly subquadratic integer 3SUM and truly subcubic APSP for polynomially bounded integer inputs.

cs.CC↗

arXiv2026

An elementary proof of the Komlós conjecture

We give an elementary proof of the Komlós conjecture by simplifying the recent proof of Guo, Fang, and Lu. We show that any vectors $v_1,\ldots,v_n\in\mathbb{R}^d$ with $\|v_i\|_2\le1$ admit signs $\varepsilon_i\in\{-1,1\}$ such that $\|\sum_{i=1}^n\varepsilon_i v_i\|_\infty\le36$. The proof uses only elementary combinatorial and probabilistic arguments and basic calculus.

math.CO↗

arXiv2026

Limitations of the slice rank method in additive combinatorics

The slice rank method gives exponential bounds for sets with no three-term arithmetic progression in finite vector spaces of odd characteristic and for three-sunflower-free families of subsets of a fixed ground set. We show that for $k\ge4$, every tensor that is nonzero exactly on the $k$-term arithmetic progression relation or the $k$-sunflower relation has maximal slice rank over every coefficient field. When the support is prescribed only on pairwise distinct inputs, we obtain comparable lower bounds, which likewise rule out exponential savings.

math.CO↗

arXiv2021

Singularity of random integer matrices with large entries

We study the singularity probability of random integer matrices. Concretely, the probability that a random $n \times n$ matrix, with integer entries chosen uniformly from $\{-m,\ldots,m\}$, is singular. This problem has been well studied in two regimes: large $n$ and constant $m$; or large $m$ and constant $n$. In this paper, we extend previous techniques to handle the regime where both $n,m$ are large. We show that the probability that such a matrix is singular is $m^{-cn}$ for some absolute constant $c>0$. We also provide some connections of our result to coding theory.

cs.CC↗

arXiv2021

Boosted Embeddings for Time Series Forecasting

Time series forecasting is a fundamental task emerging from diverse data-driven applications. Many advanced autoregressive methods such as ARIMA were used to develop forecasting models. Recently, deep learning based methods such as DeepAr, NeuralProphet, Seq2Seq have been explored for time series forecasting problem. In this paper, we propose a novel time series forecast model, DeepGB. We formulate and implement a variant of Gradient boosting wherein the weak learners are DNNs whose weights are incrementally found in a greedy manner over iterations. In particular, we develop a new embedding architecture that improves the performance of many deep learning models on time series using Gradient boosting variant. We demonstrate that our model outperforms existing comparable state-of-the-art models using real-world sensor data and public dataset.

cs.LG↗

arXiv2021

Time Series Anomaly Detection with label-free Model Selection

Anomaly detection for time-series data becomes an essential task for many data-driven applications fueled with an abundance of data and out-of-the-box machine-learning algorithms. In many real-world settings, developing a reliable anomaly model is highly challenging due to insufficient anomaly labels and the prohibitively expensive cost of obtaining anomaly examples. It imposes a significant bottleneck to evaluate model quality for model selection and parameter tuning reliably. As a result, many existing anomaly detection algorithms fail to show their promised performance after deployment. In this paper, we propose LaF-AD, a novel anomaly detection algorithm with label-free model selection for unlabeled times-series data. Our proposed algorithm performs a fully unsupervised ensemble learning across a large number of candidate parametric models. We develop a model variance metric that quantifies the sensitivity of anomaly probability with a bootstrapping method. Then it makes a collective decision for anomaly events by model learners using the model variance. Our algorithm is easily parallelizable, more robust for ill-conditioned and seasonal data, and highly scalable for a large number of anomaly models. We evaluate our algorithm against other state-of-the-art methods on a synthetic domain and a benchmark public data set.

cs.LG↗