Questions tagged [machine-learning]

Theoretical questions about Machine learning, especially Computational Learning Theory, including Algorithmic Learning Theory, PAC learning, and Bayesian Inference

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44 views

Comparision of two ML models

Let's say I have two models trained to do the same thing (EDIT : Clarification here, trained to do the same thing implies they were models trained to solve the same problem (for eg - two different ...
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Best algorithm/model to establish relevance between events utilizing mixed data type (Tags, Time, x_coordinate, y_coordinate)? [closed]

I'm building a relevance ranking system for incidents occurrence and prevention. My goal is to use four attributes to establish relevance: tag (About 500 tags), x_coordinate, y_coordinate and time. ...
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39 views

Energy-Based Modeling vs Deep Learning

I am doing some research on machine learning algorithms in the context of a seminar, which focuses on Energy-Based Modeling vs Deep Learning specifically in working with images Modeling. Now I know ...
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2answers
286 views

Circuit and Formula Lower Bounds for Separating Sparse Sets of Strings

We say that a pair $(P,N)$ of subsets of strings from $\{0,1\}^n$ is an $n$-pair if $|P|=|N|=n$. Intuitively, sucha a pair consists of a set $P$ with $n$ positive $n$-bit strings, and a set $N$ with $...
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1answer
56 views

Generalisations of the Fundamental Theorem of Statistical Learning to different tasks and losses

The fundamental theorem of statistical learning gives an equivalence between uniform convergence of the empirical risk to learning in the PAC framework. I have only seen this stated in the case of ...
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1answer
28 views

Machine Learning: Calibrating SubGroups of Probability Predictions inside a Dataset which should sum to 100%

I am working on an interesting type of problem where I want to make predicitons for individual elements within subgroups- with the knowledge that the sum of the probabilities within a subgroup should ...
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1answer
97 views

VC-dimension of infinite set of triangle wave

I am searching for the VC-dimension of the following: What is the VC-dimension of the infinite set of triangle wave functions with amplitude 1 and period parameter p on points on the line? 2πarcsin⁡(...
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1answer
113 views

What's the intuition behind Rademacher complexity?

As stated, what exactly is the intuition behind Rademacher Complexity which is defined: Rademacher complexity captures the richness of a family of functions by measuring the degree to which a ...
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1answer
145 views

How to calculate complexity in a high dimensional space?

Edit: 'Fitness landscape analysis' was mentioned as a relevant measure. If you're going to downvote the post, at least leave a comment what is wrong. For a specific f(), I'm defining a term '...
5
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1answer
212 views

Is there an equivalent to VC-dimension for density estimation as opposed to classification?

VC-dimension can be used to quantify the capacity for classifier models and compute generalization bounds, but is there an equivalent concept that can be applied to density estimation, e.g. to compute ...
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1answer
242 views

VC dimension for balanced binary decision trees

What is the VC dimension of all balanced binary decision tree of depth $k$ in $\{0,1\}^d$? Does it depend on depth $k$ or dimension $d$?
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1answer
57 views

Rademacher Complexity of the Composition with an Indicator

Consider the statistical learning setting where you have an arbitrary hypothesis space $\mathcal{H}$, a data space $\mathcal{Z}$, and a bounded loss function $\ell: \mathcal{H}\times \mathcal{Z} \...
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1answer
251 views

Testing for finite expectation

The mean of a positive random variable $X$ is either finite or infinite; define $J(X)$ to be $0$ in the former case and $1$ in the latter case. Claim: there does not exist a function $J_n$ from the ...
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68 views

Polynomial convergence to optimal move of the UCT algorithm. Missing proof?

This is a question regarding the theoretical convergence guarantees of the UCT algorithm, a popular variation of the Monte Carlo Tree Search algorithm (used in games, planning, reinforcement learning, ...
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44 views

Would a machine learning algorithm benefit from an “optimization oracle”?

I'm trying to understand the behavior of machine learning algorithms where the loss function is non-convex and the problem of training the ML on a specific data set is computationally hard. Now let'...
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42 views

Is there a notion of Probably Approximately Correctness in Unsupervised Learning? [closed]

I've been learning a little bit about computational learning theory, but most of what I've seen so far is related to supervised learning. Perhaps dimensionality reduction will be touched on, but not ...
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3answers
460 views

Reference Request: Computational Learning Theory

Pretty soon I will be finishing up Understanding Machine Learning by Shai Ben-David and Shai Shalev-Shwartz. I absolutely love the subject and want to learn more, the only issue is I'm having trouble ...
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22 views

ML classification with missing inputs using joint probability distribution

I am self-studying the deep learning book by Goodfellow, Bengio and Courville(https://www.deeplearningbook.org/contents/ml.html). On page 100, it has a brief introduction to classification with ...
2
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1answer
109 views

Why non-uniform learnability does not imply PAC learnability?

PAC guarantees provide us a a learning algorithm $A_n(\cdot)$ and sample complexity bound $n_{\mathcal{F}}(\epsilon,\sigma)$ that ensures $ P\left[L_P(A(\mathcal{D}^n))-L_P(f^*)\leq \epsilon\right]\...
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38 views

What is an example of a hard learning problem in the noisily realizable setting?

Suppose $f_{\vec{w}} : \mathbb{R}^n \rightarrow \mathbb{R}$ is a function parameterized by some parameter vector $\vec{w}$. Now for some true parameters $\vec{w}^*$, some noise function $\xi : \mathbb{...
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119 views

Understanding Dudley Chaining Argument for Rademacher Bound

I follow the proof of the Dudley chaining/metric entropy bound of the (empirical) Rademacher complexity, but I don't have any intuition for why this bound should be true. In particular, I don't know ...
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1answer
299 views

Complexity of constructing minimum depth decision trees

I am interested in the computational complexity of Problem 1: Given a finite, non-empty set $J$, given $A, B \subseteq \{0,1\}^J$ such that $A \cap B = \emptyset$, and given $n \in \mathbb{N}$, does ...
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48 views

Using martingale arguments to prove convergence of iterative algorithms

Can someone give me typical/educative examples of how martingales can be used to prove convergence of an iterative algorithmS? The examples I know of can only go so far as to show that there exists ...
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78 views

Status of the Junta Problem (soft question)

Does the learning theory community in general believe that juntas can be learned in polynomial time? The naive algorithm works in quasi-polynomial time. MOS's paper shows how to solve the junta ...
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21 views

Showing SGLD has risk minimization ability vs showing that SGLD hits SOSP

I am comparing the following 2 results, Theorem 2.1 here https://arxiv.org/abs/1702.03849 Theorem 4.3 here https://arxiv.org/abs/1904.13016 Given that the 2017 paper already shows that SGLD can ...
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1answer
202 views

Latest word on cross validation?

It's a standard result leave-one-out cross-validation is an unbiased estimator of the risk (see, e.g., Lemma 4.1 in Mohri, Rostamizadeh, Talwalkar). Are there any "better" results? Such as, say, with ...
4
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1answer
259 views

Is this a known learning problem?

Let $(\mathcal{X},\rho)$ be a metric space (say, $\mathcal{X}=[0,1]$ with the Euclidean metric). Let $\alpha:\mathcal{X}\to[0,1]$ be unknown. Suppose that $\mathcal{X}$ is endowed with a distribution $...
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1answer
118 views

Singular Value in Machine Learning

I'm reading the paper (http://proceedings.mlr.press/v9/glorot10a/glorot10a.pdf) from Glorot and Bengio. There is something that I don't understand at the abstract section on page 1. "Training may be ...
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1answer
60 views

Characterize a point cloud

Background: I have multiple point clouds (sets of objects) $\{S_i\}_{i\in\mathbb{N}}$ of variable size and "purity" (meaning that some sets contain very similar objects, some show a high diversity; ...
4
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2answers
181 views

What are some good resources for strengthening my theoretical foundation for machine learning?

I'm a computer science major and I'm taking a lot of machine learning courses. I'm finding that my theoretical foundation on subjects like calculus and linear algebra are not as strong as I'd like ...
4
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1answer
79 views

Terminology and references for a learning model

Let's say we're doing regression over $[0,1]^d$ -- either in the PAC sense with bounded-range agnostic noise or in the more classical-statistics sense with additive Gaussian noise. Suppose further ...
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49 views

Average smoothness learning rates

This question is somewhat related to this one. There are many results in statistics where convergence rates (including minimax ones) are given in terms of the smoothness properties of the underlying ...
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69 views

representation of concept classes and pac learning

I was reading the book of Kearns and Vazirani and I didn't completely understand the following: Let C be a concept class and suppose we want to PAC learn C, they say first consider a larger ...
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54 views

Which algorithms can be used to measure similarity for two very different languages?

recently I have read this paper, A Survey of text similarity approaches, and I discovered that there are a lot of algorithms that can be used to measure similarity. At present I am applying the ...
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0answers
68 views

Sentences in what kinds of grammar in the Chomsky hierarchy can be parsed by an LSTM of a given size?

Given an LSTM $N$ of a given size $A$, a sentence $S$ with a given number of words $B$, a Chomsky grammar hierarchy level $C$ in 0-3, a Chomsky grammar $G$ of level $C$ of size $D$, A given fixed, ...
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142 views

Minimum number of hours of speech needed to train a neural net to recognize speech [closed]

From a theoretical computer science point of view, is there a lower limit on the number of hours of speech needed to train a neural net to translate speech to text? An estimate from CMU is 3000-5000 ...
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84 views

Which computational framework lies behind the Chinese “Social Credit System”?

BACKGROUND The Social Credit System is a data-driven reputation system which draws on several sources to label various entities, namely businesses and individual citizens, with a trustworthiness ...
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79 views

Agnostic query learning of decision trees

Gopalan, Kalai, Klivans gave an algorithm https://dl.acm.org/citation.cfm?id=1374376.1374451 for agnostically learning decision trees $h:\{0,1\}^n\to\{0,1\}$ under the uniform distribution given ...
2
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1answer
168 views

How many samples are needed to reconstruct a path?

Consider an input set of vertices $V$ and vertices $s,t\in V$. The goal is to learn some unknown shortest path from $s$ to $t$; the set of edges of the graph is hidden at first and there may be ...
3
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1answer
79 views

Agnostic query learning for DFAs

Angluin's membership+equivalence query algorithm allows to efficiently and exactly learn a target $n$-state DFA. But what if the target DFA is huge, or the target concept is not even a regular ...
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115 views

Lower bound to agnostic learning with membership queries

Setting: Let $X$ be a finite set and $C = \{0, 1\}^X$ a finite family of classifiers on $X$. Fix an $f \in \{0, 1\}^X$ not in $C$, a (possibly randomized and adaptive) learner $A$ has access to a ...
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1answer
363 views

What was the significance of Leslie Valiant's, “A Theory of the Learnable?”

It seems like two of the main takeaways were that there is a natural limit to what computers can learn, and learning is bounded by polynomial algorithms. Why was his paper significant in the broader ...
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92 views

Machine Learning Algorithm To Fill Data Holes

I'm having trouble finding a good place to begin with this. I'm just looking for a name or point to start researching a Let's say I have 1000 records. 10 of these records are only 90% complete. The ...
2
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1answer
97 views

References on generalization bounds

I'm looking for references (books, papers, lecture notes etc) on generalization bounds and their proofs. Specifically, I'm looking to fully understand the technique of defining a hypothesis class (or ...
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1answer
32 views

Classic Neural Network Layout for regression: is the score function derivable?

I need to solve an optimization problem based on a function f(X). This function is not known, but it can be estimated from a training set. So first I train a model, then I get the score function f(X), ...
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80 views

how is time complexity defined in computational learning theory

In general, when we say an algorithm $A$ PAC learns $C$ in time $t$, we say $A$ takes time $t$ before outputting a hypothesis $h$, and the hypothesis can be evaluated (on every $x$) in time $t$. Now ...
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1answer
307 views

How to generalize VC dimension?

Let's try to generalize the $VC$-dimension (of the class of hyperplanes) to include accuracy/error. Let $S$ be a set of points in $R^d$ and $t$ in $[0,1]$. We say that the class of hyperplanes $t$-...
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1answer
141 views

Confusion about covering number

Problem I do not understand why larger $p$ will give a larger covering number. Since when $p\geq q$, the corresponding hypercube is also larger (by $\| x \| _ { q } \leq n ^ { ( 1 / q - 1 / p ) } \|...
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1answer
40 views

Does fixed hyperparameters perform well regardless the number of training examples?

I'm new in this community and I don't know whether my question is proper for this community. I will delete this post if it is not proper. I'm interested in deep learning network models and have a ...
2
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2answers
374 views

About learning a single Gaussian in total-variation distance

I am looking for the proof of this following result which I saw as being claimed as a "folklore" in a paper. It would be helpful if someone can share a reference where this has been shown! Let $G$ ...

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