The paper proves deep neural networks with analytic activation can approximate any function.
problem Approximating functions with neural networks using analytic activation functions.
method Elementary proofs for real and complex networks, Stone-Weierstrass theorem, Mergelyan's theorem.
result Closure of neural network classes equals space of polynomials for analytic activation.
Study shows sample noise impacts active learning performance.
problem Impact of sample noise on active learning performance.
method Proposed Incremental Weighted K-Means for noisy samples.
result Robust sampler improves synthetic tasks but only marginally in real-life.
This paper improves active learning for Gaussian process regression to handle distributional uncertainty.
problem Active learning for Gaussian process regression does not guarantee accurate predictions for target distributions.
method Proposes two methods to reduce worst-case expected error for Gaussian process regression.
result Shows an upper bound of the worst-case expected squared error, suggesting finite data labels can achieve arbitrarily small error.
Characterizes neural kernel and NNGP for various activations.
problem Understanding neural kernels and NNGP for non-RELU activations.
method Characterization of RKHS for various activation functions.
result Broad class of non-infinitely smooth activations generate equivalent RKHSs at different depths.
Large deviation principle for deep neural networks with ReLU activation.
problem Understanding the behavior of deep neural networks with ReLU activation.
method Proving a large deviation principle for networks with Gaussian weights and ReLU activation functions.
result Simplified expressions and power-series expansions for the ReLU case.
Study active learning of PTFs with derivative access.
problem Active learning of polynomial threshold functions (PTFs).
method Algorithm for active learning degree-d univariate PTFs with derivative access. result Computational efficient algorithm for active learning degree-d univariate PTFs. Small sample size hinders accurate long-term COVID-19 case predictions.
problem Difficulty in predicting medium and long-term COVID-19 case trends.
method Analysis of machine learning models' performance; feature selection; comparison of different models.
result Simple linear regression models provide reliable 2-week predictions but not beyond.
Improves decentralized learning by teleporting active nodes for better convergence.
problem Decentralized learning's convergence rate degrades with large node numbers.
method Activates a subset of nodes, fetches parameters from previous active nodes, updates, and performs gossip averaging on a small topology.
result Teleportation completely alleviates convergence rate degradation with proper node activation.
Data-aware activation function customization reduces neural network error.
problem Current neural networks lack consideration for specific activation functions.
method Linear algebraic explanation and Diaconis-Shahshahani Approximation Theorem criteria for activation functions.
result Using an even activation function like seagull can reduce neural network error by orders of magnitude.
Abstract: Investigates the role of activation functions in neural networks and their physical basis.
problem Understanding the role of activation functions in neural networks and their physical basis.
method Formalizes the use of activation functions in neural inference by relating them to phase transitions in statistical physics.
result Reveals the physical justification for the performance of typical activation functions in neural networks.
Bayesian adaptive designs can be biased by active learning, especially with misspecified models.
problem Active learning bias in Bayesian adaptive experimental designs.
method Analysis of linear and preference learning models, empirical testing.
result Model misspecification and noise influence active learning bias in Bayesian designs.
Method identifies cardiac ectopic activity sites from 12-lead ECG.
problem Locate dangerous ectopic activation sites in the heart.
method Bayesian optimization on cardiac model and ECG data.
result Method converges to minimum after 11.7-3.5 iterations.
In this work we propose Hebbian-descent as a biologically plausible learning rule for hetero-associative as well as auto-associative learning in single layer artificial neural networks. It can be used as a replacement for gradient descent as well as Hebbian learning, in particular in online learning, as it inherits the…
We present the first adaptive strategy for active learning in the setting of classification with smooth decision boundary. The problem of adaptivity (to unknown distributional parameters) has remained opened since the seminal work of Castro and Nowak (2007), which first established (active learning) rates for this sett…
The study proves a quantitative functional CLT for neural networks with smooth activation functions.
problem Understanding the convergence rates of neural networks with different activation functions.
method Functional versions of the Stein-Malliavin approach and a quantitative functional central limit theorem.
result Rates of convergence depend on the smoothness of the activation function, ranging from logarithmic to sqrt(n).
Improves graph-based active learning for non-Gaussian models.
problem Efficiently selecting data points for labeling in graph-based semi-supervised learning.
method Approximates non-Gaussian distributions, introduces rank-one update and model change acquisition function.
result Enhanced active learning for graph-based SSL under non-Gaussian models.
Active sampling improves design space exploration for analog circuits.
problem Efficiently exploring the space of design features in analog circuits with many parameters.
method Combining drastic dimension reduction with sensitivity analysis and Bayesian surrogate modeling for active sampling.
result The proposed active sampling flow outperforms traditional Monte-Carlo sampling.
Study shows how activation functions impact the storage capacity of treelike neural networks.
problem Understanding the role of activation functions in neural network expressive power.
method Analysis of treelike two-layer networks with various activation functions in the infinite-width limit.
result Activation functions affect storage capacity and robustness, with nonlinearity increasing capacity and decreasing robustness.
Enhances Gaussian process regression with multi-fidelity models and active subspaces for high-dimensional problems.
problem Data scarcity and high-dimensional input spaces with low intrinsic dimensionality.
method Employ Gaussian processes in a Bayesian setting, augmenting with low-fidelity models, and exploiting active subspaces.
result Improves model accuracy through multi-fidelity Gaussian process regression with active subspaces.
Researchers infer gene activity in dividing cells, accounting for protein inheritance and division history.
problem Inferring protein production kinetics in dividing cells due to protein inheritance and division history.
method Adapted conditional normalizing flows to approximate intractable likelihoods from simulated data.
result Glc3 gene is mostly inactive under stress, with brief and transient expression.
The study examines if ReLU activation function is optimal for modularity in neural networks.
problem Finding the best activation function for modularity in neural networks.
method Comparing ReLU with other activation functions for modularity and performance.
result ReLU may not be the best choice for modularity, suggesting other functions could be more suitable.
Actively sampled data can have very different characteristics than passively sampled data. Therefore, it's promising to investigate using different inference procedures during AL than are used during passive learning (PL). This general idea is explored in detail for the focused case of AL with cost-weighted SVMs for im…
Improved active output selection reduces calibration time by 10% or more.
problem Efficiently calibrate models with noisy data.
method Improved active output selection strategy considering noise estimate.
result At least 10% fewer measurements needed compared to existing strategies.
Our research focuses on analysing human activities according to a known behaviorist scenario, in case of noisy and high dimensional collected data. The data come from the monitoring of patients with dementia diseases by wearable cameras. We define a structural model of video recordings based on a Hidden Markov Model. N…
The paper proposes methods to find a shared active subspace for multivariate vector-valued functions.
problem Minimizing the deviation between function evaluations in the original and reconstructed spaces.
method Manipulating gradients or SPD matrices to identify a shared structure.
result Summing SPD matrices often identifies the best shared active subspace.
We consider two active binary-classification problems with atypical objectives. In the first, active search, our goal is to actively uncover as many members of a given class as possible. In the second, active surveying, our goal is to actively query points to ultimately predict the proportion of a given class. Numerous…
Active seriation recovers item order from noisy pairwise similarity measurements.
problem Recovering an unknown item ordering from noisy pairwise similarity measurements.
method Proposes an active seriation algorithm that provably recovers the latent ordering with high probability.
result Establishes optimal performance guarantees for successful recovery under a uniform separation condition.
ReLU is widely seen as the default choice for activation functions in neural networks. However, there are cases where more complicated functions are required. In particular, recurrent neural networks (such as LSTMs) make extensive use of both hyperbolic tangent and sigmoid functions. These functions are expensive to co…
This paper explores adaptive neural activation in RNNs for better learning.
problem Fixed neural activation functions limit the performance and adaptability of RNNs.
method Developed a novel parametric family of nonlinear activation functions inspired by biological neurons.
result Adaptive neural activation improves learning speed and performance in RNNs.
Complex-valued neural networks can approximate any continuous function with bounded widths and depths.
problem Approximating continuous functions with complex-valued neural networks of bounded widths and depths.
method Analyzing activation functions and proving universality for complex-valued networks.
result Deep narrow complex-valued networks are universal if and only if their activation function is neither holomorphic, nor antiholomorphic, nor R-affine. Logistic regression is by far the most widely used classifier in real-world applications. In this paper, we benchmark the state-of-the-art active learning methods for logistic regression and discuss and illustrate their underlying characteristics. Experiments are carried out on three synthetic datasets and 44 real-worl…
We consider active maximum a posteriori (MAP) inference problem for Hidden Markov Models (HMM), where, given an initial MAP estimate of the hidden sequence, we select to label certain states in the sequence to improve the estimation accuracy of the remaining states. We develop an analytical approach to this problem for…
Study near-maturity convergence rates of American put prices in Lévy models.
problem Analyzing convergence rates of optimal exercise prices in Lévy models.
method Examined two settings: jumps of unbounded and bounded variation, deriving near-maturity expansions.
result Near-maturity convergence rate of optimal exercise price is of order √(T-t).
Active learning methods increase classification quality by means of user feedback. An important subcategory is active learning for outlier detection with one-class classifiers. While various methods in this category exist, selecting one for a given application scenario is difficult. This is because existing methods rel…
This work establishes distribution-free upper and lower bounds on the minimax label complexity of active learning with general hypothesis classes, under various noise models. The results reveal a number of surprising facts. In particular, under the noise model of Tsybakov (2004), the minimax label complexity of active …
Improved bounds on neural network regions using activation histograms.
problem Bounding the number of affine regions in ReLU networks.
method Analysis of algebraic topology problem, extension of framework to subnetwork composition.
result Slightly tighter bounds and insights into parameter initialization.
Active inference minimizes expected free energy for optimal behavior.
problem Understanding and optimizing behavior in complex systems.
method Combines Bayesian decision theory, optimal Bayesian design, and the free energy principle.
result Active inference emerges as a unified framework for information-seeking, utility maximization, and goal-directed behavior.
Two machine learning methods detect insider trading from investor activity data.
problem Detecting insider trading from trading activity data is challenging.
method Two unsupervised machine learning methods: clustering and group identification.
result Identifies potential insider trading rings around price sensitive events.
Deep active learning improves solvability prediction in power systems.
problem Inconclusive conservatism in traditional solvability region analysis methods.
method Proposes a deep active learning framework to reduce labeled dataset size.
result Significantly reduces the size of labeled dataset for training.
New activations improve deep network reproducibility without sacrificing accuracy.
problem Deep networks' reproducibility issues, especially on distributed systems.
method Developed SmeLU activations, smoother than ReLU, to enhance reproducibility.
result SmeLU activations provide better accuracy-reproducibility tradeoffs.
We describe a framework for designing efficient active learning algorithms that are tolerant to random classification noise and are differentially-private. The framework is based on active learning algorithms that are statistical in the sense that they rely on estimates of expectations of functions of filtered random e…
PGAE uses predictions to guide active experimentation.
problem Efficiently guiding experimental sampling based on predictions.
method PGAE framework that combines predictions and actual outcomes.
result PGAE achieves asymptotic optimality and efficiency.
We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter optimization based upon marginal likelihood maximization.…
Study develops a new model for predicting individual mobility based on activity patterns.
problem Existing mobility prediction methods overlook underlying activity patterns.
method Activity-based hidden Markov model (IOHMM) using transit smart card data.
result Proposed model achieves similar prediction performance to LSTM but also provides behavioral insights.
We provide new results concerning label efficient, polynomial time, passive and active learning of linear separators. We prove that active learning provides an exponential improvement over PAC (passive) learning of homogeneous linear separators under nearly log-concave distributions. Building on this, we provide a comp…
We propose a new active learning algorithm for parametric linear regression with random design. We provide finite sample convergence guarantees for general distributions in the misspecified model. This is the first active learner for this setting that provably can improve over passive learning. Unlike other learning se…
Online purchase decisions in organizations can go through a complex journey with multiple agents involved in the decision making process. Depending on the product being purchased, and the organizational structure, the process may involve employees who first conduct market research, and then influence decision makers wh…
New algorithm learns halfspaces with membership queries, achieving near optimal label complexity.
problem Learning halfspaces with membership queries.
method Proposed a new algorithm for learning halfspaces with membership queries, proving near optimal label complexity.
result Achieves near optimal label complexity for learning halfspaces.