Approaches to learning Bayesian networks from data typically combine a scoring function with a heuristic search procedure. Given a Bayesian network structure, many of the scoring functions derived in the literature return a score for the entire equivalence class to which the structure belongs. When using such a scoring…
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48 results for “equivalence search”
LGES speeds up causal discovery while maintaining accuracy.
problem Causal discovery from observational data with computational and accuracy limitations.
method LGES modifies GES by avoiding certain edge insertions, using prior knowledge, and leveraging interventional data.
result LGES outperforms GES in speed, accuracy, and robustness to misspecified knowledge.
XGES improves GES by favoring early edge deletion, outperforming GES in finite data settings.
problem Learning directed acyclic graphs from finite data.
method Extremely Greedy Equivalent Search (XGES) improves GES by favoring early edge deletion.
result XGES consistently outperforms GES in recovering the correct graphs, and is 10 times faster.
Automates optimizer design for diverse tasks efficiently.
problem Scalability, generability, and sample efficiency in optimizer search.
method Re-arranged optimizer space into a super-tree, applying tree traversal methods.
result Discover optimizers with only 128 evaluations, surpassing human-designed and prior methods.
The search space of Bayesian Network structures is usually defined as Acyclic Directed Graphs (DAGs) and the search is done by local transformations of DAGs. But the space of Bayesian Networks is ordered by DAG Markov model inclusion and it is natural to consider that a good search policy should take this into account.…
GES algorithm improves consistency for nonparametric DAG models.
problem Consistent estimation of nonparametric DAG models.
method Greedy equivalence search with new consistency proof for nonparametric families.
result Consistency of GES for general nonparametric DAG models with smooth factorization.
Globally normalized neural sequence models are considered superior to their locally normalized equivalents because they may ameliorate the effects of label bias. However, when considering high-capacity neural parametrizations that condition on the whole input sequence, both model classes are theoretically equivalent in…
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a prob…
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a prob…
This paper proposes and evaluates the k-greedy equivalence search algorithm (KES) for learning Bayesian networks (BNs) from complete data. The main characteristic of KES is that it allows a trade-off between greediness and randomness, thus exploring different good local optima. When greediness is set at maximum, KES co…
Trust-region methods have yielded state-of-the-art results in policy search. A common approach is to use KL-divergence to bound the region of trust resulting in a natural gradient policy update. We show that the natural gradient and trust region optimization are equivalent if we use the natural parameterization of a st…
A new robust PCA method uses Innovation Search and Leverage Scores.
problem Outlier detection and robust PCA in data clustering.
method Innovation Search and Leverage Scores.
result The method provides theoretical guarantees and outperforms existing algorithms.
Casting machine learning as a type of search, we demonstrate that the proportion of problems that are favorable for a fixed algorithm is strictly bounded, such that no single algorithm can perform well over a large fraction of them. Our results explain why we must either continue to develop new learning methods year af…
Characterizes Bayesian networks up to unconditional equivalence.
problem Characterizing Bayesian networks up to unconditional equivalence.
method Transformational characterization via undirected graphs and specified moves.
result Two DAGs are in the same UEC if and only if one can be transformed into the other via a finite sequence of moves.
We present a novel view that unifies two frameworks that aim to solve sequential prediction problems: learning to search (L2S) and recurrent neural networks (RNN). We point out equivalences between elements of the two frameworks. By complementing what is missing from one framework comparing to the other, we introduce a…
We consider the problem of structure learning for bow-free acyclic path diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG models that allow for certain hidden variables. We present a first method for this problem using a greedy score-based search algorithm. We also prove some necessary and …
We present an extension of Monte Carlo Tree Search (MCTS) that strongly increases its efficiency for trees with asymmetry and/or loops. Asymmetric termination of search trees introduces a type of uncertainty for which the standard upper confidence bound (UCB) formula does not account. Our first algorithm (MCTS-T), whic…
Within machine learning, the subfield of Neural Architecture Search (NAS) has recently garnered research attention due to its ability to improve upon human-designed models. However, the computational requirements for finding an exact solution to this problem are often intractable, and the design of the search space sti…
New method detects projective equivalences and symmetries in rational 3D curves.
problem Detecting projective equivalences and symmetries in rational 3D curves.
method Using differential invariants and Möbius transformations to avoid solving large polynomial systems.
result Efficient algorithm for detecting projective equivalences and symmetries without solving large polynomial systems.
A Characterization of Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variablesstat.ME
Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Meek (1995) characterizes Markov equivalence classes for DAGs (with no latent variables) by presenting a set of orientation rules that can correctly i…
Advocates a local feedback approach for RL in unknown systems.
problem Finding optimal feedback laws in unknown nonlinear dynamical systems.
method Searches over a local feedback representation consisting of an open-loop sequence and an optimal linear feedback law.
result Results in highly efficient training and superior performance compared to global methods.
As data sets grow in size, the ability of learning methods to find structure in them is increasingly hampered by the time needed to search the large spaces of possibilities and generate a score for each that takes all of the observed data into account. For instance, Bayesian networks, the model chosen in this paper, ha…
Ordinal Causal Discoverystat.ME
New method uniquely identifies causal structure from ordinal data.
problem Challenges in causal discovery for categorical data, especially direction of relationships.
method Exploits ordinal information to uniquely identify causal structure.
result Favorable and robust performance compared to state-of-the-art methods.
New algorithms improve causal graph discovery with adaptive interventions, even under worst-case interventional costs.
problem Discover causal relationships from data with adaptive interventions and node-dependent costs.
method Define new benchmarks and provide adaptive search algorithms for causal graph discovery.
result Logarithmic approximations achieved under various settings: atomic, bounded size interventions and generalized cost objectives.
A new sampler improves the inference of causal structures from observational data.
problem Inferring causal relationships from observational data when DAGs are Markov equivalent.
method Developed a non-reversible Markov chain, Causal Zig-Zag sampler, targeting Markov Equivalence Classes of DAGs.
result The sampler improves mixing and offers efficient algorithms for DAG inference.
Discovering causal structure among a set of variables is a fundamental problem in many empirical sciences. Traditional score-based casual discovery methods rely on various local heuristics to search for a Directed Acyclic Graph (DAG) according to a predefined score function. While these methods, e.g., greedy equivalenc…
Reframed GES uses a neural conditional dependence measure for consistent causal structure learning.
problem Identifying causal structure in nonparametric settings.
method Reframed GES algorithm with a neural conditional dependence measure.
result Optimality and consistency of the reframed GES algorithm under standard assumptions.
Given a convex optimization problem and its dual, there are many possible first-order algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is done through convex duality, and implies notably that for certain problems, such…
The problem of content search through comparisons has recently received considerable attention. In short, a user searching for a target object navigates through a database in the following manner: the user is asked to select the object most similar to her target from a small list of objects. A new object list is then p…
Method detects neural network equivalence via matrix ensembles and spectral analysis.
problem Detecting equivalence among different deep learning architectures.
method Generating Mixed Matrix Ensembles (MMEs) and matching to conjugate circular ensembles.
result Empirical evidence shows vanishing differences in spectral densities with long tail decay rates.
MEC-IP uses IP to efficiently find MECs in BNs from observational data.
problem Discovering Markov Equivalent Classes (MECs) in Bayesian Networks (BNs) efficiently.
method Clique-focusing strategy and EMSG for MEC discovery via Integer Programming.
result Significant reduction in computational time and improved accuracy.
Study efficient algorithms for identifying minimum interventional sets to learn causal relationships.
problem Identify the smallest set of interventions to learn causal relationships between a subset of edges.
method Develop algorithms for subset verification and search problems under assumptions of faithfulness, causal sufficiency, and ideal interventions.
result For subset verification, an efficient algorithm is provided to compute a minimum sized interventional set.
Unified framework for sparse logistic regression with nonconvex regularization.
problem Sparse logistic regression with nonconvex regularization.
method Unified framework, line search criteria for nonconvex terms.
result Effective classification and feature selection at lower computational cost.
TF-Coder simplifies tensor manipulation programming in TensorFlow.
problem Difficulty in programming with TensorFlow due to steep learning curve.
method Bottom-up weighted enumerative search with value-based pruning and type/value filtering.
result Solves 63 out of 70 real-world tasks within 5 minutes.
Active Search has become an increasingly useful tool in information retrieval problems where the goal is to discover as many target elements as possible using only limited label queries. With the advent of big data, there is a growing emphasis on the scalability of such techniques to handle very large and very complex …
In a recent work of I.\,Dynnikov and M.\,Prasolov a new method of comparing Legendrian knots is proposed. In general, to apply the method requires a lot of technical work. In particular, one needs to search all rectangular diagrams of surfaces realizing certain dividing configurations. In this paper, it is shown that, …
The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional space into the original one, resulting in a more manageable optimization problem. S…
Network embedding algorithms are able to learn latent feature representations of nodes, transforming networks into lower dimensional vector representations. Typical key applications, which have effectively been addressed using network embeddings, include link prediction, multilabel classification and community detectio…
In iterative supervised learning algorithms it is common to reach a point in the search where no further induction seems to be possible with the available data. If the search is continued beyond this point, the risk of overfitting increases significantly. Following the recent developments in inductive semantic stochast…
SOLAR improves search efficiency and accuracy with sparse, orthogonal embeddings.
problem Bottleneck of indexing large dense vectors and NNS for query efficiency and accuracy.
method Proposes SOLAR embeddings: sparse, orthogonal, learned, and random vectors across multiple GPUs.
result Successfully trains 500K dimensional SOLAR embeddings for 1.6M books and multi-label classification.
Yau's Affine Normal Descent optimizes smooth unconstrained problems with geometrically adapted directions.
problem Optimizing smooth unconstrained problems with geometrically adapted directions.
method Yau's Affine Normal Descent (YAND) uses the equi-affine normal of level-set hypersurfaces as search directions.
result YAND converges globally under standard smoothness assumptions and locally quadratically near nondegenerate minimizers.
Study on adversarial training dynamics in high dimensions using SGD.
problem Analyzing adversarial training of models in high-dimensional settings.
method Deriving deterministic equivalents for SGD iterates under Gaussian mixtures.
result No constant learning rate guarantees monotone descent in adversarial training.
The paper refines NOTEARS for learning Bayesian networks, improving accuracy and efficiency.
problem Learning Bayesian networks from continuous optimization.
method Generalized algebraic characterizations and Karush-Kuhn-Tucker (KKT) conditions for optimization.
result Local search post-processing improves structural Hamming distance by a factor of 2 or more.
Non-parametric Determination of Real-Time Lag Structure between Two Time Series: the "Optimal Thermal Causal Path" Methodcond-mat.stat-mech
We introduce a novel non-parametric methodology to test for the dynamical time evolution of the lag-lead structure between two arbitrary time series. The method consists in constructing a distance matrix based on the matching of all sample data pairs between the two time series. Then, the lag-lead structure is searched…
Researchers study solitons on homogeneous spaces, finding useful geometric structures.
problem Finding solitons on homogeneous spaces.
method Investigating solitons with a focus on equivalence relations and optimal tangent directions.
result Solitons on homogeneous spaces have been identified as a useful tool in various geometric contexts.
Most exact methods for k-nearest neighbour search suffer from the curse of dimensionality; that is, their query times exhibit exponential dependence on either the ambient or the intrinsic dimensionality. Dynamic Continuous Indexing (DCI) offers a promising way of circumventing the curse and successfully reduces the dep…
We study a distributionally robust mean square error estimation problem over a nonconvex Wasserstein ambiguity set containing only normal distributions. We show that the optimal estimator and the least favorable distribution form a Nash equilibrium. Despite the non-convex nature of the ambiguity set, we prove that the …
Global Convergence of MAML and Theory-Inspired Neural Architecture Search for Few-Shot Learningcs.LG
MAML with over-parameterized DNNs converges globally at a linear rate.
problem Few-shot learning with limited data.
method Model-agnostic meta-learning (MAML) with over-parameterized deep neural networks (DNNs).
result MAML with over-parameterized DNNs converges globally at a linear rate.