Questions tagged [machine-learning]

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

Filter by
Sorted by
Tagged with
-2
votes
0answers
14 views

finding the probability of error of a meta-classifier

If there are two classes A and B. For a meta-classifer that classifies an instance of A, if there exists at least one independent classifier that classifies it as A. Otherwise, the meta-classifier ...
-5
votes
0answers
25 views

Is machine learning a thermodynamic cooling process? [closed]

Is there evidence or proof that machine learning is a thermodynamic cooling process and can we interpret machine learning in an information theoretic manner? What is the interpretation of stochastic ...
0
votes
0answers
36 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'...
1
vote
0answers
41 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 ...
6
votes
3answers
416 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 ...
0
votes
0answers
17 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
votes
1answer
93 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]\...
0
votes
0answers
36 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{...
3
votes
0answers
105 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 ...
7
votes
1answer
275 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 ...
0
votes
0answers
44 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 ...
4
votes
0answers
71 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 ...
0
votes
0answers
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 ...
5
votes
1answer
197 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 ...
3
votes
0answers
176 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 $...
0
votes
1answer
116 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 ...
1
vote
1answer
56 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
votes
2answers
166 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
votes
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 ...
1
vote
0answers
47 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 ...
0
votes
0answers
63 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 ...
1
vote
0answers
53 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 ...
1
vote
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, ...
1
vote
0answers
129 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 ...
2
votes
0answers
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 ...
1
vote
0answers
78 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
votes
1answer
166 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
votes
1answer
78 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 ...
0
votes
0answers
106 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 ...
4
votes
1answer
256 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 ...
-1
votes
2answers
81 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
votes
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 ...
0
votes
1answer
29 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), ...
2
votes
0answers
78 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 ...
6
votes
1answer
263 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 $t$-...
0
votes
1answer
137 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 ) } \|...
0
votes
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
votes
2answers
304 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 $G$ ...
0
votes
1answer
87 views

Lower bound of real valued bounded function

Is well known that the lower bound on number of example necessary to reach a given error for concept classes $\Omega(d/\varepsilon)$ (cf. also Agnostic PAC sampling lower bound ) I am looking for ...
2
votes
1answer
138 views

Oncina-Garcia RPNI algorithm for learning DFAs

The question refers to this paper: ftp://altea.dlsi.ua.es/people/oncina/articulos/asspr1992.pdf Given a sample of $p$ positive and $n$ negative strings, RPNI constructs a consistent DFA in time $O((p+...
1
vote
0answers
90 views

Complexity of low-rank matrix factorizations with rows in a simplex and outliers

Our goal is to obtain a matrix factorization in form of $M = U V'$, where $U\in\mathbb{R}^{d\times r}, V \in\mathbb{R}^{N\times r}$ and each row of $V$ satisfies $$ \sum_{j}(V)_{ij}=1, (V)_{ij}\ge 0 $$...
1
vote
0answers
58 views

Back-propagation for computing derivative of certain line integral

Consider a function F (think of neural networks) with two sets of parameters: (1) model parameters $\mathbf{w}$, and (2) input data ${\bf x} \in {\mathbb R}^d$. Fix $i \in [d]$, consider the following ...
4
votes
2answers
156 views

Are there hypothesis classes that are hard to learn but easy to test?

Let $H$ be a binary hypothesis class, it is easy to see that if $H$ is (efficiently) properly PAC learnable then it is also (efficiently) testable (here we use the standard notion of within or $\...
3
votes
1answer
144 views

Is there a gap between weak learning and PAC-learning?

For concreteness lets use the definitions of PAC and weak-learning as in the notes of Avrim Blum (http://www.cs.cmu.edu/~avrim/ML12/lect0208.txt) and also his notes on SQ-Learning (http://www.cs.cmu....
3
votes
0answers
106 views

Do features always induce a metric?

It is well-known in functional analysis that an inner product always induces a norm and a norm always induces a metric, and the reverse directions do not hold in general. I am wondering if a similar ...
2
votes
0answers
136 views

Crime prevention using graph theory and machine learning

I am looking for a way to the model the incidence of crime among a network of individuals. Part of it will use machine learning, and part of it will have to resort to some graph theoretic ...
7
votes
2answers
266 views

About assumptions needed to get convergence of stochastic gradient methods on non-convex objectives

What are the minimal conditions we know of under which we can prove that a stochastic gradient based algorithm can convergence to criticality on a non-convex objective? Are there any necessary ...
2
votes
1answer
103 views

Stochastic gradient methods and risk of neural nets

Under many situations it is currently provable that we can minimize the risk of neural nets using stochastic gradient based algorithms. For example : https://arxiv.org/abs/1811.03804, https://arxiv....
2
votes
1answer
103 views

Empirical Rademacher averages versus Hoeffdings bound

Let $M$ be finite set with $n$ distinct elements. I want to probalistically approximate the relative counts $\frac{|P(Q)|}{|M|}$ of $Q \subseteq M$, where $P(Q) = |P \cap M|$. An upper-bound for ...
2
votes
0answers
83 views

Lower bounds for SRM?

This question is about structural risk minimization and model selection. Let $H_n$ be the collection of all binary classifiers on some fixed set with an $n$-bit description length in some fixed ...

1
2 3 4 5
7