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Questions tagged [lg.learning]

Machine learning and learning theory: PAC learning, algorithmic learning theory, and computational aspects of Bayesian inference and graphical models.

13
votes
1answer
520 views

Reference Request: Submodular Minimization and Monotone Boolean Functions

Background: In machine learning, we often work with graphical models to represent high dimensional probability density functions. If we discard the constraint that a density integrates (sums) to 1, ...
11
votes
1answer
375 views

Agnostic learning over arbitrary distributions

Let $D$ be a distribution over bitstring/label pairs $\{0,1\}^d\times \{0,1\}$ and let $C$ be a collection of boolean valued functions $f:\{0,1\}^d\rightarrow\{0,1\}$. For each function $f \in C$, let:...
9
votes
2answers
374 views

Are there families of formal languages known to be truly PAC learnable?

I specifically mean language families that admit arbitrarily long strings -- not conjunctions over n bits or decision lists or any other "simple" language contained in {0,1}^n. I am asking about "...
41
votes
4answers
8k views

Is finding the minimum regular expression an NP-complete problem?

I am thinking of the following problem: I want to find a regular expression that matches a particular set of strings (for ex. valid email addresses) and doesn't match others (invalid email addresses). ...
5
votes
1answer
1k views

PAC learning boolean conjunctions

Kearns and Vazirani (chapter 1) describe an efficient algorithm for PAC learning conjunctions of boolean variables $x_1, x_2, \ldots, x_n$, which starts with the hypothesis $$h=x_1\wedge\overline{x_1}\...
6
votes
2answers
372 views

Online learning: Perceptron updates

It seems that the perceptron updates come from some notion of primal-dual updates for convex programs. Can anyone explain how this is true or point to relevant literature?
19
votes
2answers
527 views

Internal Regret in Online Convex Optimization

Zinkevich's "online convex optimization" ( http://www.cs.cmu.edu/~maz/publications/ICML03.pdf ) generalizes "regret minimization" learning algorithms from a linear settings to a convex setting and ...
20
votes
3answers
388 views

Property testing in other metrics?

There is a large literature on "property testing" -- the problem of making a small number of black box queries to a function $f\colon\{0,1\}^n \to R$ to distinguish between two cases: $f$ is a ...
25
votes
2answers
807 views

Approximating the sign rank of a matrix

The sign rank of a matrix A with +1,-1 entries is the least rank (over the reals) of a matrix B which has the same sign pattern as A (i.e., $A_{ij}B_{ij}>0$ for all $i,j$). This notion is important in ...
12
votes
2answers
323 views

Computational query complexity of SQ-learning

It is known that for PAC learning, there are natural concept classes (e.g. subsets of decision lists) for which there are polynomial gaps between the sample complexity needed for information theoretic ...
10
votes
5answers
3k views

What are good references on understanding online learning?

Specifically, I'm asking for resources to learn about machine learning systems that can update their respective belief networks (or equivalent) during operation. I've even run across a few, though I ...