Parameter Identifiability in Statistical Machine Learning: A Review.

Abstract:

:This review examines the relevance of parameter identifiability for statistical models used in machine learning. In addition to defining main concepts, we address several issues of identifiability closely related to machine learning, showing the advantages and disadvantages of state-of-the-art research and demonstrating recent progress. First, we review criteria for determining the parameter structure of models from the literature. This has three related issues: parameter identifiability, parameter redundancy, and reparameterization. Second, we review the deep influence of identifiability on various aspects of machine learning from theoretical and application viewpoints. In addition to illustrating the utility and influence of identifiability, we emphasize the interplay among identifiability theory, machine learning, mathematical statistics, information theory, optimization theory, information geometry, Riemann geometry, symbolic computation, Bayesian inference, algebraic geometry, and others. Finally, we present a new perspective together with the associated challenges.

journal_name

Neural Comput

journal_title

Neural computation

authors

Ran ZY,Hu BG

doi

10.1162/NECO_a_00947

subject

Has Abstract

pub_date

2017-05-01 00:00:00

pages

1151-1203

issue

5

eissn

0899-7667

issn

1530-888X

journal_volume

29

pub_type

杂志文章
  • Propagating distributions up directed acyclic graphs.

    abstract::In a previous article, we considered game trees as graphical models. Adopting an evaluation function that returned a probability distribution over values likely to be taken at a given position, we described how to build a model of uncertainty and use it for utility-directed growth of the search tree and for deciding o...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976699300016881

    authors: Baum EB,Smith WD

    更新日期:1999-01-01 00:00:00

  • Invariant global motion recognition in the dorsal visual system: a unifying theory.

    abstract::The motion of an object (such as a wheel rotating) is seen as consistent independent of its position and size on the retina. Neurons in higher cortical visual areas respond to these global motion stimuli invariantly, but neurons in early cortical areas with small receptive fields cannot represent this motion, not only...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2007.19.1.139

    authors: Rolls ET,Stringer SM

    更新日期:2007-01-01 00:00:00

  • Learning spike-based population codes by reward and population feedback.

    abstract::We investigate a recently proposed model for decision learning in a population of spiking neurons where synaptic plasticity is modulated by a population signal in addition to reward feedback. For the basic model, binary population decision making based on spike/no-spike coding, a detailed computational analysis is giv...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2010.05-09-1010

    authors: Friedrich J,Urbanczik R,Senn W

    更新日期:2010-07-01 00:00:00

  • Computing confidence intervals for point process models.

    abstract::Characterizing neural spiking activity as a function of intrinsic and extrinsic factors is important in neuroscience. Point process models are valuable for capturing such information; however, the process of fully applying these models is not always obvious. A complete model application has four broad steps: specifica...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00198

    authors: Sarma SV,Nguyen DP,Czanner G,Wirth S,Wilson MA,Suzuki W,Brown EN

    更新日期:2011-11-01 00:00:00

  • Direct estimation of inhomogeneous Markov interval models of spike trains.

    abstract::A necessary ingredient for a quantitative theory of neural coding is appropriate "spike kinematics": a precise description of spike trains. While summarizing experiments by complete spike time collections is clearly inefficient and probably unnecessary, the most common probabilistic model used in neurophysiology, the ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2009.07-08-828

    authors: Wójcik DK,Mochol G,Jakuczun W,Wypych M,Waleszczyk WJ

    更新日期:2009-08-01 00:00:00

  • Deficient GABAergic gliotransmission may cause broader sensory tuning in schizophrenia.

    abstract::We examined how the depression of intracortical inhibition due to a reduction in ambient GABA concentration impairs perceptual information processing in schizophrenia. A neural network model with a gliotransmission-mediated ambient GABA regulatory mechanism was simulated. In the network, interneuron-to-glial-cell and ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00519

    authors: Hoshino O

    更新日期:2013-12-01 00:00:00

  • Investigating the fault tolerance of neural networks.

    abstract::Particular levels of partial fault tolerance (PFT) in feedforward artificial neural networks of a given size can be obtained by redundancy (replicating a smaller normally trained network), by design (training specifically to increase PFT), and by a combination of the two (replicating a smaller PFT-trained network). Th...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/0899766053723096

    authors: Tchernev EB,Mulvaney RG,Phatak DS

    更新日期:2005-07-01 00:00:00

  • Learning only when necessary: better memories of correlated patterns in networks with bounded synapses.

    abstract::Learning in a neuronal network is often thought of as a linear superposition of synaptic modifications induced by individual stimuli. However, since biological synapses are naturally bounded, a linear superposition would cause fast forgetting of previously acquired memories. Here we show that this forgetting can be av...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/0899766054615644

    authors: Senn W,Fusi S

    更新日期:2005-10-01 00:00:00

  • Visual Categorization with Random Projection.

    abstract::Humans learn categories of complex objects quickly and from a few examples. Random projection has been suggested as a means to learn and categorize efficiently. We investigate how random projection affects categorization by humans and by very simple neural networks on the same stimuli and categorization tasks, and how...

    journal_title:Neural computation

    pub_type: 信件

    doi:10.1162/NECO_a_00769

    authors: Arriaga RI,Rutter D,Cakmak M,Vempala SS

    更新日期:2015-10-01 00:00:00

  • Synchrony of neuronal oscillations controlled by GABAergic reversal potentials.

    abstract::GABAergic synapse reversal potential is controlled by the concentration of chloride. This concentration can change significantly during development and as a function of neuronal activity. Thus, GABA inhibition can be hyperpolarizing, shunting, or partially depolarizing. Previous results pinpointed the conditions under...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2007.19.3.706

    authors: Jeong HY,Gutkin B

    更新日期:2007-03-01 00:00:00

  • Dissociable forms of repetition priming: a computational model.

    abstract::Nondeclarative memory and novelty processing in the brain is an actively studied field of neuroscience, and reducing neural activity with repetition of a stimulus (repetition suppression) is a commonly observed phenomenon. Recent findings of an opposite trend-specifically, rising activity for unfamiliar stimuli-questi...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00569

    authors: Makukhin K,Bolland S

    更新日期:2014-04-01 00:00:00

  • Time-varying perturbations can distinguish among integrate-to-threshold models for perceptual decision making in reaction time tasks.

    abstract::Several integrate-to-threshold models with differing temporal integration mechanisms have been proposed to describe the accumulation of sensory evidence to a prescribed level prior to motor response in perceptual decision-making tasks. An experiment and simulation studies have shown that the introduction of time-varyi...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2009.07-08-817

    authors: Zhou X,Wong-Lin K,Philip H

    更新日期:2009-08-01 00:00:00

  • Sparse coding on the spot: spontaneous retinal waves suffice for orientation selectivity.

    abstract::Ohshiro, Hussain, and Weliky (2011) recently showed that ferrets reared with exposure to flickering spot stimuli, in the absence of oriented visual experience, develop oriented receptive fields. They interpreted this as refutation of efficient coding models, which require oriented input in order to develop oriented re...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00333

    authors: Hunt JJ,Ibbotson M,Goodhill GJ

    更新日期:2012-09-01 00:00:00

  • Regularized neural networks: some convergence rate results.

    abstract::In a recent paper, Poggio and Girosi (1990) proposed a class of neural networks obtained from the theory of regularization. Regularized networks are capable of approximating arbitrarily well any continuous function on a compactum. In this paper we consider in detail the learning problem for the one-dimensional case. W...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.1995.7.6.1225

    authors: Corradi V,White H

    更新日期:1995-11-01 00:00:00

  • Derivatives of logarithmic stationary distributions for policy gradient reinforcement learning.

    abstract::Most conventional policy gradient reinforcement learning (PGRL) algorithms neglect (or do not explicitly make use of) a term in the average reward gradient with respect to the policy parameter. That term involves the derivative of the stationary state distribution that corresponds to the sensitivity of its distributio...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2009.12-08-922

    authors: Morimura T,Uchibe E,Yoshimoto J,Peters J,Doya K

    更新日期:2010-02-01 00:00:00

  • Learning Hough transform: a neural network model.

    abstract::A single-layered Hough transform network is proposed that accepts image coordinates of each object pixel as input and produces a set of outputs that indicate the belongingness of the pixel to a particular structure (e.g., a straight line). The network is able to learn adaptively the parametric forms of the linear segm...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976601300014501

    authors: Basak J

    更新日期:2001-03-01 00:00:00

  • Simultaneous rate-synchrony codes in populations of spiking neurons.

    abstract::Firing rates and synchronous firing are often simultaneously relevant signals, and they independently or cooperatively represent external sensory inputs, cognitive events, and environmental situations such as body position. However, how rates and synchrony comodulate and which aspects of inputs are effectively encoded...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976606774841521

    authors: Masuda N

    更新日期:2006-01-01 00:00:00

  • The effects of input rate and synchrony on a coincidence detector: analytical solution.

    abstract::We derive analytically the solution for the output rate of the ideal coincidence detector. The solution is for an arbitrary number of input spike trains with identical binomial count distributions (which includes Poisson statistics as a special case) and identical arbitrary pairwise cross-correlations, from zero corre...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976603321192068

    authors: Mikula S,Niebur E

    更新日期:2003-03-01 00:00:00

  • Patterns of synchrony in neural networks with spike adaptation.

    abstract::We study the emergence of synchronized burst activity in networks of neurons with spike adaptation. We show that networks of tonically firing adapting excitatory neurons can evolve to a state where the neurons burst in a synchronized manner. The mechanism leading to this burst activity is analyzed in a network of inte...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/08997660151134280

    authors: van Vreeswijk C,Hansel D

    更新日期:2001-05-01 00:00:00

  • Permitted and forbidden sets in symmetric threshold-linear networks.

    abstract::The richness and complexity of recurrent cortical circuits is an inexhaustible source of inspiration for thinking about high-level biological computation. In past theoretical studies, constraints on the synaptic connection patterns of threshold-linear networks were found that guaranteed bounded network dynamics, conve...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976603321192103

    authors: Hahnloser RH,Seung HS,Slotine JJ

    更新日期:2003-03-01 00:00:00

  • Spiking neural P systems with weights.

    abstract::A variant of spiking neural P systems with positive or negative weights on synapses is introduced, where the rules of a neuron fire when the potential of that neuron equals a given value. The involved values-weights, firing thresholds, potential consumed by each rule-can be real (computable) numbers, rational numbers,...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00022

    authors: Wang J,Hoogeboom HJ,Pan L,Păun G,Pérez-Jiménez MJ

    更新日期:2010-10-01 00:00:00

  • Parsing Complex Sentences with Structured Connectionist Networks.

    abstract::A modular, recurrent connectionist network is taught to incrementally parse complex sentences. From input presented one word at a time, the network learns to do semantic role assignment, noun phrase attachment, and clause structure recognition, for sentences with both active and passive constructions and center-embedd...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.1991.3.1.110

    authors: Jain AN

    更新日期:1991-04-01 00:00:00

  • Conditional density estimation with dimensionality reduction via squared-loss conditional entropy minimization.

    abstract::Regression aims at estimating the conditional mean of output given input. However, regression is not informative enough if the conditional density is multimodal, heteroskedastic, and asymmetric. In such a case, estimating the conditional density itself is preferable, but conditional density estimation (CDE) is challen...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00683

    authors: Tangkaratt V,Xie N,Sugiyama M

    更新日期:2015-01-01 00:00:00

  • A bio-inspired, computational model suggests velocity gradients of optic flow locally encode ordinal depth at surface borders and globally they encode self-motion.

    abstract::Visual navigation requires the estimation of self-motion as well as the segmentation of objects from the background. We suggest a definition of local velocity gradients to compute types of self-motion, segment objects, and compute local properties of optical flow fields, such as divergence, curl, and shear. Such veloc...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00479

    authors: Raudies F,Ringbauer S,Neumann H

    更新日期:2013-09-01 00:00:00

  • On the relation of slow feature analysis and Laplacian eigenmaps.

    abstract::The past decade has seen a rise of interest in Laplacian eigenmaps (LEMs) for nonlinear dimensionality reduction. LEMs have been used in spectral clustering, in semisupervised learning, and for providing efficient state representations for reinforcement learning. Here, we show that LEMs are closely related to slow fea...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00214

    authors: Sprekeler H

    更新日期:2011-12-01 00:00:00

  • Computing sparse representations of multidimensional signals using Kronecker bases.

    abstract::Recently there has been great interest in sparse representations of signals under the assumption that signals (data sets) can be well approximated by a linear combination of few elements of a known basis (dictionary). Many algorithms have been developed to find such representations for one-dimensional signals (vectors...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00385

    authors: Caiafa CF,Cichocki A

    更新日期:2013-01-01 00:00:00

  • Mismatched training and test distributions can outperform matched ones.

    abstract::In learning theory, the training and test sets are assumed to be drawn from the same probability distribution. This assumption is also followed in practical situations, where matching the training and test distributions is considered desirable. Contrary to conventional wisdom, we show that mismatched training and test...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00697

    authors: González CR,Abu-Mostafa YS

    更新日期:2015-02-01 00:00:00

  • Discriminant component pruning. Regularization and interpretation of multi-layered back-propagation networks.

    abstract::Neural networks are often employed as tools in classification tasks. The use of large networks increases the likelihood of the task's being learned, although it may also lead to increased complexity. Pruning is an effective way of reducing the complexity of large networks. We present discriminant components pruning (D...

    journal_title:Neural computation

    pub_type: 杂志文章,评审

    doi:10.1162/089976699300016665

    authors: Koene RA,Takane Y

    更新日期:1999-04-01 00:00:00

  • Cortical spatiotemporal dimensionality reduction for visual grouping.

    abstract::The visual systems of many mammals, including humans, are able to integrate the geometric information of visual stimuli and perform cognitive tasks at the first stages of the cortical processing. This is thought to be the result of a combination of mechanisms, which include feature extraction at the single cell level ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00738

    authors: Cocci G,Barbieri D,Citti G,Sarti A

    更新日期:2015-06-01 00:00:00

  • Resonator Networks, 2: Factorization Performance and Capacity Compared to Optimization-Based Methods.

    abstract::We develop theoretical foundations of resonator networks, a new type of recurrent neural network introduced in Frady, Kent, Olshausen, and Sommer (2020), a companion article in this issue, to solve a high-dimensional vector factorization problem arising in Vector Symbolic Architectures. Given a composite vector formed...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco_a_01329

    authors: Kent SJ,Frady EP,Sommer FT,Olshausen BA

    更新日期:2020-12-01 00:00:00