New clustering algorithms optimize Average Silhouette Width for better cluster quality.
problem Optimizing clustering using Average Silhouette Width (ASW).
method Proposed two algorithms: OSil and FOSil, compared with existing methods.
result New methods prove useful and sensible in many cases, but with some weaknesses.
OSil algorithm optimizes clustering quality using ASW.
problem Optimizing clustering quality using ASW.
method Distance-based objective function optimizing ASW for clustering.
result OSil algorithm outperforms other clustering methods in clustering quality.
Visualizes classification accuracy and label bias in neural nets and trees.
problem Identifying mislabeled cases in neural net and tree-based classifications.
method Silhouette plots and quasi residual plots of PAC (probability of alternative class).
result Comparison of different classifications using silhouette width and PAC plots.
A new method clusters malware data more effectively.
problem Difficult clustering of drive-by-download malware data.
method Iterative data rescaling method to enhance cluster separation.
result Improved separation between malware clusters, higher silhouette width.
Efficient medoid-based Silhouette method speeds up clustering evaluation.
problem Difficulty in evaluating clustering results due to many measures and data set dependence.
method Direct optimization of medoid-based Silhouette, combining PAM algorithm improvements.
result 10464x speedup in clustering evaluation for large datasets.
A new medoid-based Silhouette method selects optimal cluster numbers efficiently.
problem Difficulty in evaluating clustering results and choosing the right number of clusters.
method Developed a medoid-based Silhouette variant, analyzed its properties, and provided fast optimization methods.
result A 10464x speedup in choosing optimal cluster numbers compared to original PAMMEDSIL.
In this work, we introduce a deep-structured conditional random field (DS-CRF) model for the purpose of state-based object silhouette tracking. The proposed DS-CRF model consists of a series of state layers, where each state layer spatially characterizes the object silhouette at a particular point in time. The interact…
Enhances clustering quality evaluation in noisy data.
problem Reliable clustering quality assessment in noisy Gaussian mixtures.
method Feature Importance Rescaling (FIR) method.
result FIR improves correlation between cluster validity indices and ground truth.
This paper focuses on curves and surfaces of constant width, with some additional results about general ovals. We emphasize the use of Fourier series to derive properties, some of which are known. Amongst other results, we show that the perimeter of an oval is π times its average width, and provide a bound for the ra…
Deep forests enhance expressiveness exponentially with depth, not width or tree size.
problem Understanding the role of depth, width, and tree size in deep forest performance.
method Provided upper and lower bounds on deep forest approximation complexity.
result Depth exponentially enhances deep forest expressiveness.
Fisher width is a geometric measure of complexity on statistical manifolds.
problem Complexity measures on statistical manifolds
method Introducing Fisher width as a Fisher-geometric analogue of Gaussian width
result Fisher width retains key structural features of Gaussian width while capturing anisotropic geometric effects
Stochastic neural networks with infinite width become deterministic, reducing training variance.
problem Understanding how stochasticity in neural networks affects learning and regularization.
method Theoretical analysis of stochastic neural networks with infinite width.
result As the width of an optimized stochastic neural network increases, its predictive variance on the training set decreases to zero.
New method estimates causal effects in complex spaces using topological structures.
problem Challenges in estimating causal effects in non-Euclidean spaces.
method Developed a topological causal inference framework using power-weighted silhouette functions of persistence diagrams.
result Successfully quantifies topological treatment effects across various complex outcomes.
TDA improves FX clustering quality over traditional methods.
problem Capturing complex currency co-movements in FX markets.
method Topological Data Analysis (TDA) compared to traditional statistical methods on monthly FX returns.
result TDA-based clustering yields more compact and well-separated clusters.
The paper challenges the validity of cluster validity measures in unsupervised learning.
problem The validity of cluster validity measures in selecting optimal clusterings.
method The authors investigate the use of cluster validity measures as objective functions in unsupervised learning and introduce a new variant of the Dunn index.
result Many cluster validity measures promote clusterings that do not match expert knowledge well.
The study reveals a transition in neural network performance from infinite-width to variance-limited behavior as dataset size increases.
problem Understanding the transition from infinite-width to variance-limited behavior in neural networks.
method Empirical study of the transition from infinite-width to variance-limited behavior as a function of sample size and network width.
result The critical sample size \( P^* \) is approximately \( \sqrt{N} \) for polynomial regression with ReLU networks.
The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts of data. However, shapes represented as silhouette images are challenging to mode…
The paper investigates how irrelevant features affect clustering performance.
problem The challenge of identifying relevant features in unsupervised clustering tasks.
method Investigation of clustering performance with added irrelevant features.
result Different types of irrelevant features impact clustering outcomes differently.
We study how finite Bayesian neural networks adapt their hidden representations.
problem Understanding how finite Bayesian neural networks differ from infinite ones.
method We analyze the asymptotics of learned feature kernels for various network architectures.
result The leading finite-width corrections to feature kernels have a universal form.
Inverse depth scaling found in LLMs due to similar layers averaging error.
problem Understanding how depth affects loss in large language models.
method Analysis of LLMs and toy residual networks.
result Loss scales inversely proportional to depth in LLMs.
Obesity is an important concern in public health, and Body Mass Index is one of the useful (and proliferant) measures. We use Convolutional Neural Networks to determine Body Mass Index from photographs in a study with 161 participants. Low data, a common problem in medicine, is addressed by reducing the information in …
Paper optimizes KWS models using NAS and quantization for limited resources.
problem Developing efficient keyword spotting models in resource-constrained environments.
method Neural Architecture Search (NAS) for model structure optimization and quantization of weights and activations.
result Achieved high accuracy (95.55%) with minimal parameters and operations using NAS and quantization.
UTOPIA aggregates multiple prediction intervals efficiently.
problem Constructing optimal prediction intervals for various real-world data problems.
method UTOPIA is a universally trainable strategy using linear or convex programming.
result UTOPIA constructs prediction intervals with small average width and high coverage probability.
A new method steers Gaussian distributions with minimal effort.
problem Steering high-dimensional Gaussian distributions efficiently.
method Sliced feedback controller using one-dimensional projections and averaging.
result The method steers Gaussian distributions to targets efficiently.
This paper introduces sample-averaged Q-learning for better RL performance.
problem Improving reinforcement learning algorithms by managing uncertainty.
method Integrates statistical inference into Q-learning through sample averaging and functional central limit theorem.
result Establishes a unified theoretical foundation for sample-averaged Q-learning.
Proposes DISCO, the first CVI for density-based clustering with noise.
problem Evaluation of noise assignments in density-based clustering.
method Density-connectivity and Silhouette Coefficient adaptation for noise evaluation.
result DISCO is the first CVI to explicitly assess noise assignments.
Project aims to improve time series prediction intervals.
problem Difficulty in computing joint prediction regions for time series data.
method Wolf and Wunderli's method applied with bootstrapping and novel standard error estimation.
result Empirical evidence on the effectiveness of the method.
Equal-volume polygons are obtained from adequate discretizations of curves in 3-space, contained or not in surfaces. In this paper we explore the similarities of these polygons with the affine arc-length parameterized smooth curves to develop a theory of discrete affine invariants. Besides obtaining discrete affine inv…
Label manipulation attacks are a subclass of data poisoning attacks in adversarial machine learning used against different applications, such as malware detection. These types of attacks represent a serious threat to detection systems in environments having high noise rate or uncertainty, such as complex networks and I…
We analyze a database comprising quarterly sales of 55624 pharmaceutical products commercialized by 3939 pharmaceutical firms in the period 1992--2001. We study the probability density function (PDF) of growth in firms and product sales and find that the width of the PDF of growth decays with the sales as a power law w…
An algorithm calculates Gabai width for thousands of knots.
problem Calculating Gabai width for many knots.
method Algorithmic definition of Wirtinger width leading to efficient Gabai width bounds.
result Proved Wirtinger width equals Gabai width for knots.
Prediction intervals are a valuable way of quantifying uncertainty in regression problems. Good prediction intervals should be both correct, containing the actual value between the lower and upper bound at least a target percentage of the time; and tight, having a small mean width of the bounds. Many prior techniques f…
We consider the problem of estimating human pose and trajectory by an aerial robot with a monocular camera in near real time. We present a preliminary solution whose distinguishing feature is a dynamic classifier selection architecture. In our solution, each video frame is corrected for perspective using projective tra…
Study finds RVIs unreliable for SP selection in clustering.
problem Reliability of RVIs for selecting Similarity Paradigms (SPs) in clustering.
method Extensive experiments with 7 RVIs on synthetic and real-world datasets.
result RVIs are unreliable for SP selection.
Empirical study compares finite- and infinite-width BNNs, revealing performance differences under model mismatch.
problem Comparing BNNs with different widths due to conflicting model properties and inference intractability.
method Empirical comparison of finite- and infinite-width BNNs, analyzing performance under model mismatch.
result Increasing width can hurt BNN performance when the model is mis-specified, and finite-width BNNs generalize better under model mismatch.
A novel resampling technique addresses class imbalance in imbalanced datasets.
problem Class imbalance in real-world datasets, especially in rare event detection.
method Developed two oversampling algorithms: G1Nos 1-Nearest Neighbour.
result Our oversampling algorithms outperform state-of-the-art methods in all metrics.
Study clusters bank customers using LSTM and DTW.
problem Efficiently segmenting bank customers for targeted offers.
method Encoder-decoder LSTM network and Dynamic Time Warping (DTW).
result Hybrid method yields more accurate clusters.
Skew-adaptive method improves prediction intervals for regression.
problem Improving prediction intervals for regression models, especially in cases of skewness and varying scales.
method Develops a skew-adaptive extension of split conformal prediction using an asymmetric interval family and gauge approach.
result Preserves marginal validity and adapts to local scale and skewness, with efficiency gains over existing methods.
The isospectral problem for p-widths is solved using Zoll metrics on S^2.
problem Determine if a Riemannian manifold is uniquely determined by its p-widths.
method Construct counterexamples on S^2 using Zoll metrics and properties of geodesic p-widths.
result Many counterexamples exist on S^2, showing uniqueness is not guaranteed.
Congealing is a flexible nonparametric data-driven framework for the joint alignment of data. It has been successfully applied to the joint alignment of binary images of digits, binary images of object silhouettes, grayscale MRI images, color images of cars and faces, and 3D brain volumes. This research enhances congea…
Width trees link link invariants and bridge number.
problem Understanding link invariants through geometric structures.
method Associate width trees to links and use their geometric properties to bound link invariants.
result Width trees uniquely realize certain link invariants under specific conditions.
Before training a neural net, a classic rule of thumb is to randomly initialize the weights so the variance of activations is preserved across layers. This is traditionally interpreted using the total variance due to randomness in both weights \emph{and} samples. Alternatively, one can interpret the rule of thumb as pr…
Lectures on deep learning properties in infinite and large-width networks.
problem Understanding deep neural networks in extreme width conditions.
method Analysis of random deep neural networks, connections to linear models, kernels, and Gaussian processes, perturbative and non-perturbative treatments.
result Properties and behaviors of deep neural networks in the infinite-width limit and large-width regime.
Computed p-widths for hemisphere, first for manifolds with boundary.
problem Finding p-widths for manifolds with boundary.
method Computed p-widths for the hemisphere.
result First known p-widths for a manifold with boundary.
Polygon p-widths are found via billiard trajectories.
problem Finding p-widths of polygons. method Proved via billiard trajectories and computed specific cases.
result Polygon p-widths are achieved by billiard trajectories. A number of results for C2-smooth surfaces of constant width in Euclidean 3-space E3 are obtained. In particular, an integral inequality for constant width surfaces is established. This is used to prove that the ratio of volume to cubed width of a constant width surface is reduced by shrinking it along…
Computed p-widths for real projective plane.
problem Calculating p-widths for real projective plane.
method Standard metric used to compute p-widths.
result Computed p-widths for real projective plane.
Study bounds Urysohn width of manifolds under surgeries.
problem Bounding Urysohn width of manifolds after surgeries.
method Analyzes connected sums and universal covers, applies to general surgeries.
result Optimal constants in estimates of width bounds are shown.